{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "name": "Ch2_MorePyMC_TFP.ipynb", "version": "0.3.2", "provenance": [], "collapsed_sections": [] }, "kernelspec": { "name": "python3", "display_name": "Python 3" }, "accelerator": "GPU" }, "cells": [ { "metadata": { "colab_type": "text", "id": "phBEJ8iLIAwF" }, "cell_type": "markdown", "source": [ "# Probabilistic Programming and Bayesian Methods for Hackers Chapter 2\n", "\n", "\n", " \n", " \n", "
\n", " Run in Google Colab\n", " \n", " View source on GitHub\n", "
\n", "
\n", "
\n", "
\n", "\n", "Original content ([this Jupyter notebook](https://nbviewer.jupyter.org/github/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/blob/master/Chapter2_MorePyMC/Ch2_MorePyMC_PyMC2.ipynb)) created by Cam Davidson-Pilon ([`@Cmrn_DP`](https://twitter.com/Cmrn_DP))\n", "\n", "Ported to [Tensorflow Probability](https://www.tensorflow.org/probability/) by Matthew McAteer ([`@MatthewMcAteer0`](https://twitter.com/MatthewMcAteer0)), with help from Bryan Seybold, Mike Shwe ([`@mikeshwe`](https://twitter.com/mikeshwe)), Josh Dillon, and the rest of the TFP team at Google ([`tfprobability@tensorflow.org`](mailto:tfprobability@tensorflow.org)).\n", "\n", "Welcome to Bayesian Methods for Hackers. The full Github repository is available at [github/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers). The other chapters can be found on the project's [homepage](https://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/). We hope you enjoy the book, and we encourage any contributions!\n", "___\n", "\n", "### Table of Contents\n", "\n", "- Dependencies & Prerequisites\n", "- A little more on TFP\n", " - TFP Variables\n", " - Initializing Stochastic Variables\n", " - Deterministic variables\n", " - Combining with Tensorflow Core\n", " - Including observations in the Model\n", "- Modeling approaches\n", " - Same story; different ending\n", " - Example: Bayesian A/B testing\n", " - A Simple Case\n", " - Execute the TF graph to sample from the posterior\n", " - A and B together\n", " - Execute the TF graph to sample from the posterior\n", "- An algorithm for human deceit\n", " - The Binomial Distribution\n", " - Example: Cheating among students\n", " - Execute the TF graph to sample from the posterior\n", " - Alternative TFP Model\n", " - Execute the TF graph to sample from the posterior\n", " - More TFP Tricks\n", " - Example: Challenger Space Shuttle Disaster\n", " - Normal Distributions\n", " - Execute the TF graph to sample from the posterior\n", " - What about the day of the Challenger disaster?\n", " - Is our model appropriate?\n", " - Execute the TF graph to sample from the posterior\n", " - Exercises\n", " - References\n", "___\n", "\n", "This chapter introduces more TFP syntax and variables and ways to think about how to model a system from a Bayesian perspective. It also contains tips and data visualization techniques for assessing goodness-of-fit for your Bayesian model." ] }, { "metadata": { "colab_type": "text", "id": "AIIO6GhdH89m" }, "cell_type": "markdown", "source": [ "### Dependencies & Prerequisites\n", "\n", "
\n", " Tensorflow Probability is part of the colab default runtime, so you don't need to install Tensorflow or Tensorflow Probability if you're running this in the colab. \n", "
\n", " If you're running this notebook in Jupyter on your own machine (and you have already installed Tensorflow), you can use the following\n", "
\n", " \n", "Again, if you are running this in a Colab, Tensorflow and TFP are already installed\n", "
" ] }, { "metadata": { "colab_type": "code", "id": "jFKYjxy1IAwG", "outputId": "91a30576-d9c6-47be-fcfc-a81e4304b46f", "colab": { "base_uri": "https://localhost:8080/", "height": 161 } }, "cell_type": "code", "source": [ "#@title Imports and Global Variables (run this cell first) { display-mode: \"form\" }\n", "\"\"\"\n", "The book uses a custom matplotlibrc file, which provides the unique styles for\n", "matplotlib plots. If executing this book, and you wish to use the book's\n", "styling, provided are two options:\n", " 1. Overwrite your own matplotlibrc file with the rc-file provided in the\n", " book's styles/ dir. See http://matplotlib.org/users/customizing.html\n", " 2. Also in the styles is bmh_matplotlibrc.json file. This can be used to\n", " update the styles in only this notebook. Try running the following code:\n", "\n", " import json\n", " s = json.load(open(\"../styles/bmh_matplotlibrc.json\"))\n", " matplotlib.rcParams.update(s)\n", "\"\"\"\n", "!pip3 install -q wget\n", "from __future__ import absolute_import, division, print_function\n", "#@markdown This sets the warning status (default is `ignore`, since this notebook runs correctly)\n", "warning_status = \"ignore\" #@param [\"ignore\", \"always\", \"module\", \"once\", \"default\", \"error\"]\n", "import warnings\n", "warnings.filterwarnings(warning_status)\n", "with warnings.catch_warnings():\n", " warnings.filterwarnings(warning_status, category=DeprecationWarning)\n", " warnings.filterwarnings(warning_status, category=UserWarning)\n", "\n", "import numpy as np\n", "import os\n", "#@markdown This sets the styles of the plotting (default is styled like plots from [FiveThirtyeight.com](https://fivethirtyeight.com/))\n", "matplotlib_style = 'fivethirtyeight' #@param ['fivethirtyeight', 'bmh', 'ggplot', 'seaborn', 'default', 'Solarize_Light2', 'classic', 'dark_background', 'seaborn-colorblind', 'seaborn-notebook']\n", "import matplotlib.pyplot as plt; plt.style.use(matplotlib_style)\n", "import matplotlib.axes as axes;\n", "from matplotlib.patches import Ellipse\n", "%matplotlib inline\n", "import seaborn as sns; sns.set_context('notebook')\n", "from IPython.core.pylabtools import figsize\n", "#@markdown This sets the resolution of the plot outputs (`retina` is the highest resolution)\n", "notebook_screen_res = 'retina' #@param ['retina', 'png', 'jpeg', 'svg', 'pdf']\n", "%config InlineBackend.figure_format = notebook_screen_res\n", "\n", "import tensorflow as tf\n", "tfe = tf.contrib.eager\n", "\n", "# Eager Execution\n", "#@markdown Check the box below if you want to use [Eager Execution](https://www.tensorflow.org/guide/eager)\n", "#@markdown Eager execution provides An intuitive interface, Easier debugging, and a control flow comparable to Numpy. You can read more about it on the [Google AI Blog](https://ai.googleblog.com/2017/10/eager-execution-imperative-define-by.html)\n", "use_tf_eager = False #@param {type:\"boolean\"}\n", "\n", "# Use try/except so we can easily re-execute the whole notebook.\n", "if use_tf_eager:\n", " try:\n", " tf.enable_eager_execution()\n", " except:\n", " pass\n", "\n", "import tensorflow_probability as tfp\n", "tfd = tfp.distributions\n", "tfb = tfp.bijectors\n", "\n", " \n", "def evaluate(tensors):\n", " \"\"\"Evaluates Tensor or EagerTensor to Numpy `ndarray`s.\n", " Args:\n", " tensors: Object of `Tensor` or EagerTensor`s; can be `list`, `tuple`,\n", " `namedtuple` or combinations thereof.\n", "\n", " Returns:\n", " ndarrays: Object with same structure as `tensors` except with `Tensor` or\n", " `EagerTensor`s replaced by Numpy `ndarray`s.\n", " \"\"\"\n", " if tf.executing_eagerly():\n", " return tf.contrib.framework.nest.pack_sequence_as(\n", " tensors,\n", " [t.numpy() if tf.contrib.framework.is_tensor(t) else t\n", " for t in tf.contrib.framework.nest.flatten(tensors)])\n", " return sess.run(tensors)\n", "\n", "class _TFColor(object):\n", " \"\"\"Enum of colors used in TF docs.\"\"\"\n", " red = '#F15854'\n", " blue = '#5DA5DA'\n", " orange = '#FAA43A'\n", " green = '#60BD68'\n", " pink = '#F17CB0'\n", " brown = '#B2912F'\n", " purple = '#B276B2'\n", " yellow = '#DECF3F'\n", " gray = '#4D4D4D'\n", " def __getitem__(self, i):\n", " return [\n", " self.red,\n", " self.orange,\n", " self.green,\n", " self.blue,\n", " self.pink,\n", " self.brown,\n", " self.purple,\n", " self.yellow,\n", " self.gray,\n", " ][i % 9]\n", "TFColor = _TFColor()\n", "\n", "def session_options(enable_gpu_ram_resizing=True, enable_xla=True):\n", " \"\"\"\n", " Allowing the notebook to make use of GPUs if they're available.\n", " \n", " XLA (Accelerated Linear Algebra) is a domain-specific compiler for linear \n", " algebra that optimizes TensorFlow computations.\n", " \"\"\"\n", " config = tf.ConfigProto()\n", " config.log_device_placement = True\n", " if enable_gpu_ram_resizing:\n", " # `allow_growth=True` makes it possible to connect multiple colabs to your\n", " # GPU. Otherwise the colab malloc's all GPU ram.\n", " config.gpu_options.allow_growth = True\n", " if enable_xla:\n", " # Enable on XLA. https://www.tensorflow.org/performance/xla/.\n", " config.graph_options.optimizer_options.global_jit_level = (\n", " tf.OptimizerOptions.ON_1)\n", " return config\n", "\n", "\n", "def reset_sess(config=None):\n", " \"\"\"\n", " Convenience function to create the TF graph & session or reset them.\n", " \"\"\"\n", " if config is None:\n", " config = session_options()\n", " global sess\n", " tf.reset_default_graph()\n", " try:\n", " sess.close()\n", " except:\n", " pass\n", " sess = tf.InteractiveSession(config=config)\n", "\n", "reset_sess()" ], "execution_count": 1, "outputs": [ { "output_type": "stream", "text": [ " Building wheel for wget (setup.py) ... \u001b[?25ldone\n", "\u001b[?25h\n", "WARNING: The TensorFlow contrib module will not be included in TensorFlow 2.0.\n", "For more information, please see:\n", " * https://github.com/tensorflow/community/blob/master/rfcs/20180907-contrib-sunset.md\n", " * https://github.com/tensorflow/addons\n", "If you depend on functionality not listed there, please file an issue.\n", "\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "24368dz9IAwM" }, "cell_type": "markdown", "source": [ "## A little more on TensorFlow and TensorFlow Probability\n", "\n", "To explain TensorFlow Probability, it's worth going into the various methods of working with Tensorflow tensors. Here, we introduce the notion of Tensorflow graphs and how we can use certain coding patterns to make our tensor-processing workflows much faster and more elegant. " ] }, { "metadata": { "colab_type": "text", "id": "tOj8bjBmNuxm" }, "cell_type": "markdown", "source": [ "### TensorFlow Graph and Eager Modes\n", "\n", "TFP accomplishes most of its heavy lifting via the main `tensorflow` library. The `tensorflow` library also contains many of the familiar computational elements of NumPy and uses similar notation. While NumPy directly executes computations (e.g. when you run `a + b`), `tensorflow` in graph mode instead builds up a \"compute graph\" that tracks that you want to perform the `+` operation on the elements `a` and `b`. Only when you evaluate a `tensorflow` expression does the computation take place--`tensorflow` is lazy evaluated. The benefit of using Tensorflow over NumPy is that the graph enables mathematical optimizations (e.g. simplifications), gradient calculations via automatic differentiation, compiling the entire graph to C to run at machine speed, and also compiling it to run on a GPU or TPU. \n", "\n", "Fundamentally, TensorFlow uses [graphs](https://www.tensorflow.org/guide/graphs) for computation, wherein the graphs represent computation as dependencies among individual operations. In the programming paradigm for Tensorflow graphs, we first define the dataflow graph, and then create a TensorFlow session to run parts of the graph. A Tensorflow [`tf.Session()`](https://www.tensorflow.org/api_docs/python/tf/Session) object runs the graph to get the variables we want to model. In the example below, we are using a global session object `sess`, which we created above in the \"Imports and Global Variables\" section. \n", "\n", "To avoid the sometimes confusing aspects of lazy evaluation, Tensorflow's eager mode does immediate evaluation of results to give an even more similar feel to working with NumPy. With Tensorflow [eager](https://www.tensorflow.org/guide/eager) mode, you can evaluate operations immediately, without explicitly building graphs: operations return concrete values instead of constructing a computational graph to run later. If we're in eager mode, we are presented with tensors that can be converted to NumPy array equivalents immediately. Eager mode makes it easy to get started with TensorFlow and debug models.\n", "\n", "\n", "TFP is essentially:\n", "\n", "* a collection of tensorflow symbolic expressions for various probability distributions that are combined into one big compute graph, and\n", "* a collection of inference algorithms that use that graph to compute probabilities and gradients.\n", "\n", "For practical purposes, what this means is that in order to build certain models we sometimes have to use core Tensorflow. This simple example for Poisson sampling is how we might work with both graph and eager modes:" ] }, { "metadata": { "colab_type": "code", "id": "CmiGas0kXiEw", "outputId": "a7788041-8cab-4868-bada-fdd89062bb1a", "colab": { "base_uri": "https://localhost:8080/", "height": 35 } }, "cell_type": "code", "source": [ "parameter = tfd.Exponential(rate=1., name=\"poisson_param\").sample()\n", "rv_data_generator = tfd.Poisson(parameter, name=\"data_generator\")\n", "data_generator = rv_data_generator.sample()\n", "\n", "if tf.executing_eagerly():\n", " data_generator_ = tf.contrib.framework.nest.pack_sequence_as(\n", " data_generator,\n", " [t.numpy() if tf.contrib.framework.is_tensor(t) else t\n", " for t in tf.contrib.framework.nest.flatten(data_generator)])\n", "else:\n", " data_generator_ = sess.run(data_generator)\n", " \n", "print(\"Value of sample from data generator random variable:\", data_generator_)" ], "execution_count": 2, "outputs": [ { "output_type": "stream", "text": [ "Value of sample from data generator random variable: 2.0\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "9kArT4GTIAwT" }, "cell_type": "markdown", "source": [ "In graph mode, Tensorflow will automatically assign any variables to a graph; they can then be evaluated in a session or made available in eager mode. If you try to define a variable when the session is already closed or in a finalized state, you will get an error. In the \"Imports and Global Variables\" section, we defined a particular type of session, called [`InteractiveSession`](https:///www.tensorflow.org/api_docs/python/tf/InteractiveSession). \n", "This definition of a global `InteractiveSession` allows us to access our session variables interactively via a shell or notebook." ] }, { "metadata": { "colab_type": "text", "id": "4IEk40NbIAwX" }, "cell_type": "markdown", "source": [ "Using the pattern of a global session, we can incrementally build a graph and run subsets of it to get the results.\n", "\n", "Eager execution further simplifies our code, eliminating the need to call session functions explicitly. In fact, if you try to run graph mode semantics in eager mode, you will get an error message like this:\n", "\n", "```\n", "AttributeError: Tensor.graph is meaningless when eager execution is enabled.\n", "```\n", "\n", "As mentioned in the previous chapter, we have a nifty tool that allows us to create code that's usable in both graph mode and eager mode. The custom `evaluate()` function allows us to evaluate tensors whether we are operating in TF graph or eager mode. A generalization of our data generator example above, the function looks like the following:\n", "\n", "```python\n", "\n", "def evaluate(tensors):\n", " if tf.executing_eagerly():\n", " return tf.contrib.framework.nest.pack_sequence_as(\n", " tensors,\n", " [t.numpy() if tf.contrib.framework.is_tensor(t) else t\n", " for t in tf.contrib.framework.nest.flatten(tensors)])\n", " with tf.Session() as sess:\n", " return sess.run(tensors)\n", "\n", "```\n", "\n", "Each of the tensors corresponds to a NumPy-like output. To distinguish the tensors from their NumPy-like counterparts, we will use the convention of appending an underscore to the version of the tensor that one can use NumPy-like arrays on. In other words, the output of `evaluate()` gets named as `variable` + `_` = `variable_` . Now, we can do our Poisson sampling using both the `evaluate()` function and this new convention for naming Python variables in TFP." ] }, { "metadata": { "colab_type": "code", "id": "Bk-vyPB9IAwX", "outputId": "44667dae-aa3f-49d0-d25d-c47815c40714", "colab": { "base_uri": "https://localhost:8080/", "height": 53 } }, "cell_type": "code", "source": [ "# Defining our Assumptions\n", "parameter = tfd.Exponential(rate=1., name=\"poisson_param\").sample()\n", "\n", "# Converting our TF to Numpy\n", "[ parameter_ ] = evaluate([ parameter ])\n", "\n", "print(\"Sample from exponential distribution before evaluation: \", parameter)\n", "print(\"Evaluated sample from exponential distribution: \", parameter_)" ], "execution_count": 3, "outputs": [ { "output_type": "stream", "text": [ "Sample from exponential distribution before evaluation: Tensor(\"poisson_param_1/sample/Reshape:0\", shape=(), dtype=float32)\n", "Evaluated sample from exponential distribution: 0.011206482\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "ZlGWIiPLIAwo" }, "cell_type": "markdown", "source": [ "More generally, we can use our `evaluate()` function to convert between the Tensorflow `tensor` data type and one that we can run operations on:" ] }, { "metadata": { "colab_type": "code", "id": "1tzQmnsFIAwp", "outputId": "281c282d-abbd-42ef-8a2f-e8762747741b", "colab": { "base_uri": "https://localhost:8080/", "height": 53 } }, "cell_type": "code", "source": [ "[ \n", " parameter_,\n", " data_generator_,\n", "] = evaluate([ \n", " parameter, \n", " data_generator,\n", "])\n", "\n", "print(\"'parameter_' evaluated Tensor :\", parameter_)\n", "print(\"'data_generator_' sample evaluated Tensor :\", data_generator_)\n" ], "execution_count": 4, "outputs": [ { "output_type": "stream", "text": [ "'parameter_' evaluated Tensor : 1.3005725\n", "'data_generator_' sample evaluated Tensor : 1.0\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "m0PLxpCIc--r" }, "cell_type": "markdown", "source": [ "\n", "A general rule of thumb for programming in TensorFlow is that if you need to do any array-like calculations that would require NumPy functions, you should use their equivalents in TensorFlow. This practice is necessary because NumPy can produce only constant values but TensorFlow tensors are a dynamic part of the computation graph. If you mix and match these the wrong way, you will typically get an error about incompatible types." ] }, { "metadata": { "colab_type": "text", "id": "wqkS8vztNoyh" }, "cell_type": "markdown", "source": [ "### TFP Distributions\n", "\n", "Let's look into how [`tfp.distributions`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions) work.\n", "\n", "TFP uses distribution subclasses to represent *stochastic*, random variables. A variable is stochastic when the following is true: even if you knew all the values of the variable's parameters and components, it would still be random. Included in this category are instances of classes [`Poisson`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Poisson), [`Uniform`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Uniform), and [`Exponential`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Exponential).\n", "\n", "You can draw random samples from a stochastic variable. When you draw samples, those samples become [`tensorflow.Tensors`](https://www.tensorflow.org/api_docs/python/tf/Tensor) that behave deterministically from that point on. A quick mental check to determine if something is *deterministic* is: *If I knew all of the inputs for creating the variable `foo`, I could calculate the value of `foo`.* You can add, subtract, and otherwise manipulate the tensors in a variety of ways discussed below. These operations are almost always deterministic.\n" ] }, { "metadata": { "colab_type": "text", "id": "NdKiqWtWIAwy" }, "cell_type": "markdown", "source": [ "#### Initializing a Distribution\n", "\n", "Initializing a stochastic, or random, variable requires a few class-specific parameters that describe the Distribution's shape, such as the location and scale. For example:\n", "\n", "```python\n", "some_distribution = tfd.Uniform(0., 4.)\n", "```\n", "\n", "initializes a stochastic, or random, [`Uniform`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Uniform) distribution with the lower bound at 0 and upper bound at 4. Calling `sample()` on the distribution returns a tensor that will behave deterministically from that point on:\n", "\n", "```python\n", "sampled_tensor = some_distribution.sample()\n", "```\n", "\n", "The next example demonstrates what we mean when we say that distributions are stochastic but tensors are deterministic:\n", "\n", "```\n", "derived_tensor_1 = 1 + sampled_tensor\n", "derived_tensor_2 = 1 + sampled_tensor # equal to 1\n", "\n", "derived_tensor_3 = 1 + some_distribution.sample()\n", "derived_tensor_4 = 1 + some_distribution.sample() # different from 3\n", "```\n", "\n", "The first two lines produce the same value because they refer to the same sampled tensor. The last two lines likely produce different values because they refer to independent samples drawn from the same distribution.\n", "\n", "To define a multiviariate distribution, just pass in arguments with the shape you want the output to be when creating the distribution. For example:\n", "\n", "```python\n", "betas = tfd.Uniform([0., 0.], [1., 1.])\n", "```\n", "\n", "Creates a Distribution with batch_shape (2,). Now, when you call betas.sample(),\n", "two values will be returned instead of one. You can read more about TFP shape semantics in the [TFP docs](https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Understanding_TensorFlow_Distributions_Shapes.ipynb), but most uses in this book should be self-explanatory." ] }, { "metadata": { "colab_type": "text", "id": "UPt9k8YrIAwz" }, "cell_type": "markdown", "source": [ "#### Deterministic variables\n", "\n", "We can create a deterministic distribution similarly to how we create a stochastic distribution. We simply call up the [`Deterministic`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Deterministic) class from Tensorflow Distributions and pass in the deterministic value that we desire\n", "```python\n", "deterministic_variable = tfd.Deterministic(name=\"deterministic_variable\", loc=some_function_of_variables)\n", "```\n", "\n", "Calling `tfd.Deterministic` is useful for creating distributions that always have the same value. However, the much more common pattern for working with deterministic variables in TFP is to create a tensor or sample from a distribution:" ] }, { "metadata": { "colab_type": "code", "id": "feDM_HX6IAw0", "colab": {} }, "cell_type": "code", "source": [ "lambda_1 = tfd.Exponential(rate=1., name=\"lambda_1\") #stochastic variable\n", "lambda_2 = tfd.Exponential(rate=1., name=\"lambda_2\") #stochastic variable\n", "tau = tfd.Uniform(name=\"tau\", low=0., high=10.) #stochastic variable\n", "\n", "# deterministic variable since we are getting results of lambda's after sampling \n", "new_deterministic_variable = tfd.Deterministic(name=\"deterministic_variable\", \n", " loc=(lambda_1.sample() + lambda_2.sample()))" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "text", "id": "cRzLJmAJIAw3" }, "cell_type": "markdown", "source": [ "The use of the deterministic variable was seen in the previous chapter's text-message example. Recall the model for $\\lambda$ looked like: \n", "\n", "$$\n", "\\lambda = \n", "\\begin{cases}\\lambda_1 & \\text{if } t \\lt \\tau \\cr\n", "\\lambda_2 & \\text{if } t \\ge \\tau\n", "\\end{cases}\n", "$$\n", "\n", "And in TFP code:" ] }, { "metadata": { "colab_type": "code", "id": "IXdTQeqrIAw3", "outputId": "08ee59df-b3fe-4400-8019-c314715bc49e", "colab": { "base_uri": "https://localhost:8080/", "height": 127 } }, "cell_type": "code", "source": [ "# Build graph\n", "\n", "# days\n", "n_data_points = 5 # in CH1 we had ~70 data points\n", "idx = np.arange(n_data_points)\n", "# for n_data_points samples, select from lambda_2 if sampled tau >= day value, lambda_1 otherwise\n", "rv_lambda_deterministic = tfd.Deterministic(tf.gather([lambda_1.sample(), lambda_2.sample()],\n", " indices=tf.to_int32(\n", " tau.sample() >= idx)))\n", "lambda_deterministic = rv_lambda_deterministic.sample()\n", "\n", "# Execute graph\n", "[lambda_deterministic_] = evaluate([lambda_deterministic])\n", "\n", "# Show results\n", "\n", "print(\"{} samples from our deterministic lambda model: \\n\".format(n_data_points), lambda_deterministic_ )" ], "execution_count": 6, "outputs": [ { "output_type": "stream", "text": [ "WARNING:tensorflow:From :6: to_int32 (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n", "Instructions for updating:\n", "Use tf.cast instead.\n", "5 samples from our deterministic lambda model: \n", " [1.0830135 1.0830135 1.0830135 0.03013135 0.03013135]\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "EFgJwLATIAw8" }, "cell_type": "markdown", "source": [ "Clearly, if $\\tau, \\lambda_1$ and $\\lambda_2$ are known, then $\\lambda$ is known completely, hence it is a deterministic variable. We use indexing here to switch from $\\lambda_1$ to $\\lambda_2$ at the appropriate time. " ] }, { "metadata": { "colab_type": "text", "id": "IMNdtRTtIAxB" }, "cell_type": "markdown", "source": [ "### Including observations in the model\n", "\n", "At this point, it may not look like it, but we have fully specified our priors. For example, we can ask and answer questions like \"What does my prior distribution of $\\lambda_1$ look like?\" \n", "\n", "To do this, we will sample from the distribution. The method `.sample()` has a very simple role: get data points from the given distribution. We can then evaluate the resulting tensor to get a NumPy array-like object. " ] }, { "metadata": { "colab_type": "code", "id": "VNdQVTSFIAxC", "outputId": "5e44d4b8-9ef5-4f3a-9512-fb29ad4a995e", "colab": { "base_uri": "https://localhost:8080/", "height": 393 } }, "cell_type": "code", "source": [ "# Define our observed samples\n", "rv_lambda_1 = tfd.Exponential(rate=1., name=\"lambda_1\")\n", "lambda_1 = rv_lambda_1.sample(sample_shape=20000)\n", " \n", "# Execute graph, convert TF to NumPy\n", "[ lambda_1_ ] = evaluate([ lambda_1 ])\n", "\n", "# Visualize our stepwise prior distribution\n", "plt.figure(figsize(12.5, 5))\n", "plt.hist(lambda_1_, bins=70, density=True, histtype=\"stepfilled\")\n", "plt.title(r\"Prior distribution for $\\lambda_1$\")\n", "plt.xlim(0, 8);" ], "execution_count": 7, "outputs": [ { "output_type": "stream", "text": [ "/usr/local/lib/python3.6/dist-packages/matplotlib/axes/_axes.py:6521: MatplotlibDeprecationWarning: \n", "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n", " alternative=\"'density'\", removal=\"3.1\")\n" ], "name": "stderr" }, { "output_type": "display_data", "data": { "image/png": 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" ] }, "metadata": { "tags": [], "image/png": { "width": 828, "height": 322 } } } ] }, { "metadata": { "colab_type": "text", "id": "9nOs9Gq3IAxH" }, "cell_type": "markdown", "source": [ "To frame this in the notation of the first chapter, though this is a slight abuse of notation, we have specified $P(A)$. Our next goal is to include data/evidence/observations $X$ into our model. \n", "\n", "Sometimes we may want to match a property of our distribution to a property of observed data. To do so, we get the parameters for our distribution fom the data itself. In this example, the Poisson rate (average number of events) is explicitly set to one over the average of the data:" ] }, { "metadata": { "colab_type": "code", "id": "qtHXSR6QIAxH", "outputId": "e7e49f0e-3868-4b6d-af29-5e489afc9a18", "colab": { "base_uri": "https://localhost:8080/", "height": 143 } }, "cell_type": "code", "source": [ "# Build graph\n", "data = tf.constant([10., 5.], dtype=tf.float32)\n", "rv_poisson = tfd.Poisson(rate=1./tf.reduce_mean(data))\n", "poisson = rv_poisson.sample()\n", "\n", "# Execute graph\n", "[ data_, poisson_, ] = evaluate([ data, poisson ])\n", "\n", "# Show results\n", "print(\"two predetermined data points: \", data_)\n", "print(\"\\n mean of our data: \", np.mean(data_))\n", "print(\"\\n random sample from poisson distribution \\n with the mean as the poisson's rate: \\n\", poisson_)" ], "execution_count": 8, "outputs": [ { "output_type": "stream", "text": [ "two predetermined data points: [10. 5.]\n", "\n", " mean of our data: 7.5\n", "\n", " random sample from poisson distribution \n", " with the mean as the poisson's rate: \n", " 0.0\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "8oxo5VcbIAxP" }, "cell_type": "markdown", "source": [ "## Modeling approaches\n", "\n", "A good starting thought to Bayesian modeling is to think about *how your data might have been generated*. Position yourself in an omniscient position, and try to imagine how *you* would recreate the dataset. \n", "\n", "In the last chapter we investigated text message data. We begin by asking how our observations may have been generated:\n", "\n", "1. We started by thinking \"what is the best random variable to describe this count data?\" A Poisson random variable is a good candidate because it can represent count data. So we model the number of sms's received as sampled from a Poisson distribution.\n", "\n", "2. Next, we think, \"Ok, assuming sms's are Poisson-distributed, what do I need for the Poisson distribution?\" Well, the Poisson distribution has a parameter $\\lambda$. \n", "\n", "3. Do we know $\\lambda$? No. In fact, we have a suspicion that there are *two* $\\lambda$ values, one for the earlier behaviour and one for the later behaviour. We don't know when the behaviour switches though, but call the switchpoint $\\tau$.\n", "\n", "4. What is a good distribution for the two $\\lambda$s? The exponential is good, as it assigns probabilities to positive real numbers. Well the exponential distribution has a parameter too, call it $\\alpha$.\n", "\n", "5. Do we know what the parameter $\\alpha$ might be? No. At this point, we could continue and assign a distribution to $\\alpha$, but it's better to stop once we reach a set level of ignorance: whereas we have a prior belief about $\\lambda$, (\"it probably changes over time\", \"it's likely between 10 and 30\", etc.), we don't really have any strong beliefs about $\\alpha$. So it's best to stop here. \n", "\n", " What is a good value for $\\alpha$ then? We think that the $\\lambda$s are between 10-30, so if we set $\\alpha$ really low (which corresponds to larger probability on high values) we are not reflecting our prior well. Similar, a too-high alpha misses our prior belief as well. A good idea for $\\alpha$ as to reflect our belief is to set the value so that the mean of $\\lambda$, given $\\alpha$, is equal to our observed mean. This was shown in the last chapter.\n", "\n", "6. We have no expert opinion of when $\\tau$ might have occurred. So we will suppose $\\tau$ is from a discrete uniform distribution over the entire timespan.\n", "\n", "\n", "Below we give a graphical visualization of this, where arrows denote `parent-child` relationships. (provided by the [Daft Python library](http://daft-pgm.org/) )\n", "\n", "\n", "\n", "\n", "TFP and other probabilistic programming languages have been designed to tell these data-generation *stories*. More generally, B. Cronin writes [2]:\n", "\n", "> Probabilistic programming will unlock narrative explanations of data, one of the holy grails of business analytics and the unsung hero of scientific persuasion. People think in terms of stories - thus the unreasonable power of the anecdote to drive decision-making, well-founded or not. But existing analytics largely fails to provide this kind of story; instead, numbers seemingly appear out of thin air, with little of the causal context that humans prefer when weighing their options." ] }, { "metadata": { "colab_type": "text", "id": "3RJEK_yjIAxR" }, "cell_type": "markdown", "source": [ "### Same story; different ending.\n", "\n", "Interestingly, we can create *new datasets* by retelling the story.\n", "For example, if we reverse the above steps, we can simulate a possible realization of the dataset.\n", "\n", "1\\. Specify when the user's behaviour switches by sampling from $\\text{DiscreteUniform}(0, 80)$:" ] }, { "metadata": { "colab_type": "code", "id": "Ma56S7r1IAxS", "outputId": "0f39f444-ceb4-4cb3-dfb9-da0529bb72fc", "colab": { "base_uri": "https://localhost:8080/", "height": 35 } }, "cell_type": "code", "source": [ "tau = tf.random_uniform(shape=[1], minval=0, maxval=80, dtype=tf.int32)\n", "\n", "[ tau_ ] = evaluate([ tau ])\n", "\n", "print(\"Value of Tau (randomly taken from DiscreteUniform(0, 80)):\", tau_)" ], "execution_count": 9, "outputs": [ { "output_type": "stream", "text": [ "Value of Tau (randomly taken from DiscreteUniform(0, 80)): [71]\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "Xt_6sYG6IAxW" }, "cell_type": "markdown", "source": [ "2\\. Draw $\\lambda_1$ and $\\lambda_2$ from a $\\text{Gamma}(\\alpha)$ distribution:\n", "\n", "Note: A gamma distribution is a generalization of the exponential distribution. A gamma distribution with shape parameter $α = 1$ and scale parameter $β$ is an exponential ($β$) distribution. Here, we use a gamma distribution to have more flexibility than we would have had were we to model with an exponential. Rather than returning values between $0$ and $1$, we can return values much larger than $1$ (i.e., the kinds of numbers one would expect to show up in a daily SMS count)." ] }, { "metadata": { "colab_type": "code", "id": "l2QX3nEbofZr", "outputId": "9bc5a1b7-36a8-420b-975c-84b1f087e8ec", "colab": { "base_uri": "https://localhost:8080/", "height": 53 } }, "cell_type": "code", "source": [ "alpha = 1./8.\n", "\n", "lambdas = tfd.Gamma(concentration=1/alpha, rate=0.3).sample(sample_shape=[2]) \n", "[ lambda_1_, lambda_2_ ] = evaluate( lambdas )\n", "print(\"Lambda 1 (randomly taken from Gamma(α) distribution): \", lambda_1_)\n", "print(\"Lambda 2 (randomly taken from Gamma(α) distribution): \", lambda_2_)" ], "execution_count": 10, "outputs": [ { "output_type": "stream", "text": [ "Lambda 1 (randomly taken from Gamma(α) distribution): 19.056139\n", "Lambda 2 (randomly taken from Gamma(α) distribution): 21.798222\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "uIoKaO4bIAxb" }, "cell_type": "markdown", "source": [ "3\\. For days before $\\tau$, represent the user's received SMS count by sampling from $\\text{Poi}(\\lambda_1)$, and sample from $\\text{Poi}(\\lambda_2)$ for days after $\\tau$. For example:" ] }, { "metadata": { "colab_type": "code", "id": "6xxOtwxvpk_P", "outputId": "a3b32970-4b82-4eae-e66b-b61d2d39e0e9", "colab": { "base_uri": "https://localhost:8080/", "height": 125 } }, "cell_type": "code", "source": [ "data = tf.concat([tfd.Poisson(rate=lambda_1_).sample(sample_shape=tau_),\n", " tfd.Poisson(rate=lambda_2_).sample(sample_shape= (80 - tau_))], axis=0)\n", "days_range = tf.range(80)\n", "[ data_, days_range_ ] = evaluate([ data, days_range ])\n", "print(\"Artificial day-by-day user SMS count created by sampling: \\n\", data_)" ], "execution_count": 11, "outputs": [ { "output_type": "stream", "text": [ "Artificial day-by-day user SMS count created by sampling: \n", " [19. 24. 24. 19. 16. 22. 22. 24. 24. 18. 23. 17. 13. 14. 13. 18. 16. 14.\n", " 24. 20. 14. 22. 17. 21. 23. 18. 22. 16. 19. 22. 15. 18. 22. 16. 15. 22.\n", " 26. 12. 17. 22. 16. 24. 16. 17. 21. 20. 21. 19. 24. 14. 21. 22. 25. 20.\n", " 18. 22. 25. 20. 18. 17. 19. 22. 20. 26. 29. 23. 17. 17. 20. 14. 9. 14.\n", " 17. 27. 23. 23. 18. 18. 25. 25.]\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "5PWuas1oIAxg" }, "cell_type": "markdown", "source": [ "4\\. Plot the artificial dataset:" ] }, { "metadata": { "colab_type": "code", "id": "vrGXdyZyIAxh", "outputId": "9e67ca72-9de8-4457-c3a9-f606a1940b82", "colab": { "base_uri": "https://localhost:8080/", "height": 354 } }, "cell_type": "code", "source": [ "plt.bar(days_range_, data_, color=TFColor[3])\n", "plt.bar(tau_ - 1, data_[tau_ - 1], color=\"r\", label=\"user behaviour changed\")\n", "plt.xlabel(\"Time (days)\")\n", "plt.ylabel(\"count of text-msgs received\")\n", "plt.title(\"Artificial dataset\")\n", "plt.xlim(0, 80)\n", "plt.legend();" ], "execution_count": 12, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "tags": [], "image/png": { "width": 843, "height": 337 } } } ] }, { "metadata": { "colab_type": "text", "id": "ulb46iQIIAxn" }, "cell_type": "markdown", "source": [ "It is okay that our fictional dataset does not look like our observed dataset: the probability is incredibly small it indeed would. TFP's engine is designed to find good parameters, $\\lambda_i, \\tau$, that maximize this probability. \n", "\n", "\n", "The ability to generate an artificial dataset is an interesting side effect of our modeling, and we will see that this ability is a very important method of Bayesian inference. We produce a few more datasets below:" ] }, { "metadata": { "colab_type": "code", "id": "vrLFYvVzIAxp", "outputId": "df211715-2f83-4847-beb8-68105006dc34", "colab": { "base_uri": "https://localhost:8080/", "height": 488 } }, "cell_type": "code", "source": [ "def plot_artificial_sms_dataset(): \n", " tau = tf.random_uniform(shape=[1], \n", " minval=0, \n", " maxval=80,\n", " dtype=tf.int32)\n", " alpha = 1./8.\n", " lambdas = tfd.Gamma(concentration=1/alpha, rate=0.3).sample(sample_shape=[2]) \n", " [ lambda_1_, lambda_2_ ] = evaluate( lambdas )\n", " data = tf.concat([tfd.Poisson(rate=lambda_1_).sample(sample_shape=tau),\n", " tfd.Poisson(rate=lambda_2_).sample(sample_shape= (80 - tau))], axis=0)\n", " days_range = tf.range(80)\n", " \n", " [ \n", " tau_,\n", " data_,\n", " days_range_,\n", " ] = evaluate([ \n", " tau,\n", " data,\n", " days_range,\n", " ])\n", " \n", " plt.bar(days_range_, data_, color=TFColor[3])\n", " plt.bar(tau_ - 1, data_[tau_ - 1], color=\"r\", label=\"user behaviour changed\")\n", " plt.xlim(0, 80);\n", "\n", "plt.figure(figsize(12.5, 8))\n", "for i in range(4):\n", " plt.subplot(4, 1, i+1)\n", " plot_artificial_sms_dataset()\n" ], "execution_count": 13, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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" ] }, "metadata": { "tags": [], "image/png": { "width": 827, "height": 471 } } } ] }, { "metadata": { "colab_type": "text", "id": "V8QMiJXOIAxv" }, "cell_type": "markdown", "source": [ "Later we will see how we use this to make predictions and test the appropriateness of our models." ] }, { "metadata": { "colab_type": "text", "id": "2lU8C4C-IAxw" }, "cell_type": "markdown", "source": [ "### Example: Bayesian A/B testing\n", "\n", "A/B testing is a statistical design pattern for determining the difference of effectiveness between two different treatments. For example, a pharmaceutical company is interested in the effectiveness of drug A vs drug B. The company will test drug A on some fraction of their trials, and drug B on the other fraction (this fraction is often 1/2, but we will relax this assumption). After performing enough trials, the in-house statisticians sift through the data to determine which drug yielded better results. \n", "\n", "Similarly, front-end web developers are interested in which design of their website yields more sales or some other metric of interest. They will route some fraction of visitors to site A, and the other fraction to site B, and record if the visit yielded a sale or not. The data is recorded (in real-time), and analyzed afterwards. \n", "\n", "Often, the post-experiment analysis is done using something called a hypothesis test like *difference of means test* or *difference of proportions test*. This involves often misunderstood quantities like a \"Z-score\" and even more confusing \"p-values\" (please don't ask). If you have taken a statistics course, you have probably been taught this technique (though not necessarily *learned* this technique). And if you were like me, you may have felt uncomfortable with their derivation -- good: the Bayesian approach to this problem is much more natural. \n" ] }, { "metadata": { "colab_type": "text", "id": "AFcmkQEyDgyK" }, "cell_type": "markdown", "source": [ "### A Simple Case\n", "\n", "As this is a hacker book, we'll continue with the web-dev example. For the moment, we will focus on the analysis of site A only. Assume that there is some true $0 \\lt p_A \\lt 1$ probability that users who, upon shown site A, eventually purchase from the site. This is the true effectiveness of site A. Currently, this quantity is unknown to us. \n", "\n", "Suppose site A was shown to $N$ people, and $n$ people purchased from the site. One might conclude hastily that $p_A = \\frac{n}{N}$. Unfortunately, the *observed frequency* $\\frac{n}{N}$ does not necessarily equal $p_A$ -- there is a difference between the *observed frequency* and the *true frequency* of an event. The true frequency can be interpreted as the probability of an event occurring. For example, the true frequency of rolling a 1 on a 6-sided die is $\\frac{1}{6}$. Knowing the true frequency of events like:\n", "\n", "- fraction of users who make purchases, \n", "- frequency of social attributes, \n", "- percent of internet users with cats etc. \n", "\n", "are common requests we ask of Nature. Unfortunately, often Nature hides the true frequency from us and we must *infer* it from observed data.\n", "\n", "The *observed frequency* is then the frequency we observe: say rolling the die 100 times you may observe 20 rolls of 1. The observed frequency, 0.2, differs from the true frequency, $\\frac{1}{6}$. We can use Bayesian statistics to infer probable values of the true frequency using an appropriate prior and observed data.\n", "\n", "\n", "With respect to our A/B example, we are interested in using what we know, $N$ (the total trials administered) and $n$ (the number of conversions), to estimate what $p_A$, the true frequency of buyers, might be. \n", "\n", "To setup a Bayesian model, we need to assign prior distributions to our unknown quantities. *A priori*, what do we think $p_A$ might be? For this example, we have no strong conviction about $p_A$, so for now, let's assume $p_A$ is uniform over $[0,1]$:" ] }, { "metadata": { "colab_type": "code", "id": "blTLKyo2IAxy", "colab": {} }, "cell_type": "code", "source": [ "reset_sess()\n", "\n", "# The parameters are the bounds of the Uniform.\n", "rv_p = tfd.Uniform(low=0., high=1., name='p')\n" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "text", "id": "f0XLF9h3IAx2" }, "cell_type": "markdown", "source": [ "Had we had stronger beliefs, we could have expressed them in the prior above.\n", "\n", "For this example, consider $p_A = 0.05$, and $N = 1500$ users shown site A, and we will simulate whether the user made a purchase or not. To simulate this from $N$ trials, we will use a *Bernoulli* distribution: if $X\\ \\sim \\text{Ber}(p)$, then $X$ is 1 with probability $p$ and 0 with probability $1 - p$. Of course, in practice we do not know $p_A$, but we will use it here to simulate the data. We can assume then that we can use the following generative model:\n", "\n", "$$\\begin{align*}\n", "p &\\sim \\text{Uniform}[\\text{low}=0,\\text{high}=1) \\\\\n", "X\\ &\\sim \\text{Bernoulli}(\\text{prob}=p) \\\\\n", "\\text{for } i &= 1\\ldots N:\\text{# Users} \\\\\n", " X_i\\ &\\sim \\text{Bernoulli}(p_i)\n", "\\end{align*}$$" ] }, { "metadata": { "colab_type": "code", "id": "riLrk5KTIAx4", "outputId": "f38e999d-2c7a-40e5-a269-ea34a1fb0bee", "colab": { "base_uri": "https://localhost:8080/", "height": 71 } }, "cell_type": "code", "source": [ "reset_sess()\n", "\n", "#set constants\n", "prob_true = 0.05 # remember, this is unknown.\n", "N = 1500\n", "\n", "# sample N Bernoulli random variables from Ber(0.05).\n", "# each random variable has a 0.05 chance of being a 1.\n", "# this is the data-generation step\n", "\n", "occurrences = tfd.Bernoulli(probs=prob_true).sample(sample_shape=N, seed=10)\n", "occurrences_sum = tf.reduce_sum(occurrences)\n", "occurrences_mean = tf.reduce_mean(tf.cast(occurrences,tf.float32))\n", "\n", "[ \n", " occurrences_,\n", " occurrences_sum_,\n", " occurrences_mean_,\n", "] = evaluate([ \n", " occurrences, \n", " occurrences_sum,\n", " occurrences_mean,\n", "])\n", "\n", "print(\"Array of {} Occurences:\".format(N), occurrences_) \n", "print(\"(Remember: Python treats True == 1, and False == 0)\")\n", "print(\"Sum of (True == 1) Occurences:\", occurrences_sum_)" ], "execution_count": 15, "outputs": [ { "output_type": "stream", "text": [ "Array of 1500 Occurences: [0 0 0 ... 0 1 0]\n", "(Remember: Python treats True == 1, and False == 0)\n", "Sum of (True == 1) Occurences: 76\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "UpJrMifMIAx7" }, "cell_type": "markdown", "source": [ "The observed frequency is:" ] }, { "metadata": { "colab_type": "code", "id": "trjtemdNIAx7", "outputId": "4ce20790-4eed-4386-e02a-ebd1f797791e", "colab": { "base_uri": "https://localhost:8080/", "height": 53 } }, "cell_type": "code", "source": [ "# Occurrences.mean is equal to n/N.\n", "print(\"What is the observed frequency in Group A? %.4f\" % occurrences_mean_)\n", "print(\"Does this equal the true frequency? %s\" % (occurrences_mean_ == prob_true))" ], "execution_count": 16, "outputs": [ { "output_type": "stream", "text": [ "What is the observed frequency in Group A? 0.0507\n", "Does this equal the true frequency? False\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "Gue-SRTYIAyA" }, "cell_type": "markdown", "source": [ "We can combine our Bernoulli distribution and our observed occurrences into a log probability function based on the two." ] }, { "metadata": { "colab_type": "code", "id": "Ct9o0w7lGaZb", "colab": {} }, "cell_type": "code", "source": [ "def joint_log_prob(occurrences, prob_A):\n", " \"\"\"\n", " Joint log probability optimization function.\n", " \n", " Args:\n", " occurrences: An array of binary values (0 & 1), representing \n", " the observed frequency\n", " prob_A: scalar estimate of the probability of a 1 appearing \n", " Returns: \n", " sum of the joint log probabilities from all of the prior and conditional distributions\n", " \"\"\" \n", " rv_prob_A = tfd.Uniform(low=0., high=1.)\n", " rv_occurrences = tfd.Bernoulli(probs=prob_A)\n", " return (\n", " rv_prob_A.log_prob(prob_A)\n", " + tf.reduce_sum(rv_occurrences.log_prob(occurrences))\n", " )" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "text", "id": "UN7Mh5U-uFye" }, "cell_type": "markdown", "source": [ "The goal of probabilistic inference is to find model parameters that may explain\n", "data you have observed. TFP performs probabilistic inference by evaluating the\n", "model parameters using a `joint_log_prob` function. The arguments to `joint_log_prob` are data and model parameters—for the model defined in the `joint_log_prob` function itself. The function returns the log of the joint probability that the model parameterized as such generated the observed data per the input arguments.\n", "\n", "All `joint_log_prob` functions have a common structure:\n", "\n", "1. The function takes a set of **inputs** to evaluate. Each input is either an\n", "observed value or a model parameter.\n", "\n", "1. The `joint_log_prob` function uses probability distributions to define a **model** for evaluating the inputs. These distributions measure the likelihood of the input values. (By convention, the distribution that measures the likelihood of the variable `foo` will be named `rv_foo` to note that it is a random variable.) We use two types of distributions in `joint_log_prob` functions:\n", "\n", " a. **Prior distributions** measure the likelihood of input values.\n", "A prior distribution never depends on an input value. Each prior distribution measures the\n", "likelihood of a single input value. Each unknown variable—one that has not been\n", "observed directly—needs a corresponding prior. Beliefs about which values could\n", "be reasonable determine the prior distribution. Choosing a prior can be tricky,\n", "so we will cover it in depth in Chapter 6.\n", "\n", " b. **Conditional distributions** measure the likelihood of an input value given\n", "other input values. Typically, the conditional\n", "distributions return the likelihood of observed data given the current guess of parameters in the model, p(observed_data | model_parameters).\n", "\n", "1. Finally, we calculate and return the **joint log probability** of the inputs.\n", "The joint log probability is the sum of the log probabilities from all of the\n", "prior and conditional distributions. (We take the sum of log probabilities\n", "instead of multiplying the probabilities directly for reasons of numerical\n", "stability: floating point numbers in computers cannot represent the very small\n", "values necessary to calculate the joint log probability unless they are in \n", "log space.) The sum of probabilities is actually an unnormalized density; although the total sum of probabilities over all possible inputs might not sum to one, the sum of probabilities is proportional to the true probability density. This proportional distribution is sufficient to estimate the distribution of likely inputs.\n", "\n", "Let's map these terms onto the code above. In this example, the input values\n", "are the observed values in `occurrences` and the unknown value for `prob_A`. The `joint_log_prob` takes the current guess for `prob_A`\n", "and answers, how likely is the data if `prob_A` is the probability of\n", "`occurrences`. The answer depends on two distributions:\n", "1. The prior distribution, `rv_prob_A`, indicates how likely the current value of `prob_A` is by itself.\n", "2. The conditional distribution, `rv_occurrences`, indicates the likelihood of `occurrences` if `prob_A` were the probability for the Bernoulli distribution.\n", "\n", "The sum of the log of these probabilities is the\n", "joint log probability. \n", "\n", "The `joint_log_prob` is particularly useful in conjunction with the [`tfp.mcmc`](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc)\n", "module. Markov chain Monte Carlo (MCMC) algorithms proceed by making educated guesses about the unknown\n", "input values and\n", "computing what the likelihood of this set of arguments is. (We’ll talk about how it makes those guesses in Chapter 3.) By repeating this process\n", "many times, MCMC builds a distribution of likely parameters. Constructing this\n", "distribution is the goal of probabilistic inference." ] }, { "metadata": { "colab_type": "text", "id": "rzm3amOgDAGg" }, "cell_type": "markdown", "source": [ "Then we run our inference algorithm:" ] }, { "metadata": { "colab_type": "code", "id": "g9XHX0h8IAyB", "outputId": "918d273a-1ba3-4920-c068-9864d0b00faa", "colab": { "base_uri": "https://localhost:8080/", "height": 145 } }, "cell_type": "code", "source": [ "number_of_steps = 48000 #@param {type:\"slider\", min:2000, max:50000, step:100}\n", "#@markdown (Default is 18000).\n", "burnin = 25000 #@param {type:\"slider\", min:0, max:30000, step:100}\n", "#@markdown (Default is 1000).\n", "leapfrog_steps=2 #@param {type:\"slider\", min:1, max:9, step:1}\n", "#@markdown (Default is 6).\n", "\n", "# Set the chain's start state.\n", "initial_chain_state = [\n", " tf.reduce_mean(tf.to_float(occurrences)) \n", " * tf.ones([], dtype=tf.float32, name=\"init_prob_A\")\n", "]\n", "\n", "# Since HMC operates over unconstrained space, we need to transform the\n", "# samples so they live in real-space.\n", "unconstraining_bijectors = [\n", " tfp.bijectors.Identity() # Maps R to R. \n", "]\n", "\n", "# Define a closure over our joint_log_prob.\n", "# The closure makes it so the HMC doesn't try to change the `occurrences` but\n", "# instead determines the distributions of other parameters that might generate\n", "# the `occurrences` we observed.\n", "unnormalized_posterior_log_prob = lambda *args: joint_log_prob(occurrences, *args)\n", "\n", "# Initialize the step_size. (It will be automatically adapted.)\n", "with tf.variable_scope(tf.get_variable_scope(), reuse=tf.AUTO_REUSE):\n", " step_size = tf.get_variable(\n", " name='step_size',\n", " initializer=tf.constant(0.5, dtype=tf.float32),\n", " trainable=False,\n", " use_resource=True\n", " )\n", "\n", "# Defining the HMC\n", "hmc = tfp.mcmc.TransformedTransitionKernel(\n", " inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(\n", " target_log_prob_fn=unnormalized_posterior_log_prob,\n", " num_leapfrog_steps=leapfrog_steps,\n", " step_size=step_size,\n", " step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(num_adaptation_steps=int(burnin * 0.8)),\n", " state_gradients_are_stopped=True),\n", " bijector=unconstraining_bijectors)\n", "\n", "# Sampling from the chain.\n", "[\n", " posterior_prob_A\n", "], kernel_results = tfp.mcmc.sample_chain(\n", " num_results=number_of_steps,\n", " num_burnin_steps=burnin,\n", " current_state=initial_chain_state,\n", " kernel=hmc)\n", "\n", "# Initialize any created variables.\n", "init_g = tf.global_variables_initializer()\n", "init_l = tf.local_variables_initializer()" ], "execution_count": 18, "outputs": [ { "output_type": "stream", "text": [ "WARNING:tensorflow:From :10: to_float (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n", "Instructions for updating:\n", "Use tf.cast instead.\n", "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/python/ops/resource_variable_ops.py:435: colocate_with (from tensorflow.python.framework.ops) is deprecated and will be removed in a future version.\n", "Instructions for updating:\n", "Colocations handled automatically by placer.\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "yUVnbqhDVfAx" }, "cell_type": "markdown", "source": [ "#### Execute the TF graph to sample from the posterior" ] }, { "metadata": { "colab_type": "code", "id": "Q3By4GWdEtQN", "outputId": "2b54d312-7002-474b-cbe1-68a83057eadf", "colab": { "base_uri": "https://localhost:8080/", "height": 35 } }, "cell_type": "code", "source": [ "evaluate(init_g)\n", "evaluate(init_l)\n", "[\n", " posterior_prob_A_,\n", " kernel_results_,\n", "] = evaluate([\n", " posterior_prob_A,\n", " kernel_results,\n", "])\n", "\n", " \n", "print(\"acceptance rate: {}\".format(\n", " kernel_results_.inner_results.is_accepted.mean()))\n", "\n", "burned_prob_A_trace_ = posterior_prob_A_[burnin:]" ], "execution_count": 19, "outputs": [ { "output_type": "stream", "text": [ "acceptance rate: 0.46827083333333336\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "MQUWTY7-LgGv" }, "cell_type": "markdown", "source": [ "We plot the posterior distribution of the unknown $p_A$ below:" ] }, { "metadata": { "colab_type": "code", "id": "w_P52-CRFJPs", "outputId": "5d35d8fd-c137-43ef-c4d7-b692541f08d1", "colab": { "base_uri": "https://localhost:8080/", "height": 338 } }, "cell_type": "code", "source": [ "plt.figure(figsize(12.5, 4))\n", "plt.title(\"Posterior distribution of $p_A$, the true effectiveness of site A\")\n", "plt.vlines(prob_true, 0, 90, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n", "plt.hist(burned_prob_A_trace_, bins=25, histtype=\"stepfilled\", density=True)\n", "plt.legend();" ], "execution_count": 20, "outputs": [ { "output_type": "stream", "text": [ "/usr/local/lib/python3.6/dist-packages/matplotlib/axes/_axes.py:6521: MatplotlibDeprecationWarning: \n", "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n", " alternative=\"'density'\", removal=\"3.1\")\n" ], "name": "stderr" }, { "output_type": "display_data", "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "tags": [], "image/png": { "width": 823, "height": 267 } } } ] }, { "metadata": { "colab_type": "text", "id": "LdLJ2iriIAyI" }, "cell_type": "markdown", "source": [ "Our posterior distribution puts most weight near the true value of $p_A$, but also some weights in the tails. This is a measure of how uncertain we should be, given our observations. Try changing the number of observations, `N`, and observe how the posterior distribution changes.\n", "\n", "### *A* and *B* Together\n", "\n", "A similar analysis can be done for site B's response data to determine the analogous $p_B$. But what we are really interested in is the *difference* between $p_A$ and $p_B$. Let's infer $p_A$, $p_B$, *and* $\\text{delta} = p_A - p_B$, all at once. We can do this using TFP's deterministic variables. (We'll assume for this exercise that $p_B = 0.04$, so $\\text{delta} = 0.01$, $N_B = 750$ (significantly less than $N_A$) and we will simulate site B's data like we did for site A's data ). Our model now looks like the following:\n", "\n", "$$\\begin{align*}\n", "p_A &\\sim \\text{Uniform}[\\text{low}=0,\\text{high}=1) \\\\\n", "p_B &\\sim \\text{Uniform}[\\text{low}=0,\\text{high}=1) \\\\\n", "X\\ &\\sim \\text{Bernoulli}(\\text{prob}=p) \\\\\n", "\\text{for } i &= 1\\ldots N: \\\\\n", " X_i\\ &\\sim \\text{Bernoulli}(p_i)\n", "\\end{align*}$$" ] }, { "metadata": { "colab_type": "code", "id": "yPDLHl6RIAyJ", "outputId": "35f82e1b-56d9-4428-dc6e-938f31cea821", "colab": { "base_uri": "https://localhost:8080/", "height": 89 } }, "cell_type": "code", "source": [ "reset_sess()\n", "\n", "#these two quantities are unknown to us.\n", "true_prob_A_ = 0.05\n", "true_prob_B_ = 0.04\n", "\n", "#notice the unequal sample sizes -- no problem in Bayesian analysis.\n", "N_A_ = 1500\n", "N_B_ = 750\n", "\n", "#generate some observations\n", "observations_A = tfd.Bernoulli(name=\"obs_A\", \n", " probs=true_prob_A_).sample(sample_shape=N_A_, seed=6.45)\n", "observations_B = tfd.Bernoulli(name=\"obs_B\", \n", " probs=true_prob_B_).sample(sample_shape=N_B_, seed=6.45)\n", "[ \n", " observations_A_,\n", " observations_B_,\n", "] = evaluate([ \n", " observations_A, \n", " observations_B, \n", "])\n", "\n", "print(\"Obs from Site A: \", observations_A_[:30], \"...\")\n", "print(\"Observed Prob_A: \", np.mean(observations_A_), \"...\")\n", "print(\"Obs from Site B: \", observations_B_[:30], \"...\")\n", "print(\"Observed Prob_B: \", np.mean(observations_B_))" ], "execution_count": 21, "outputs": [ { "output_type": "stream", "text": [ "Obs from Site A: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n", "Observed Prob_A: 0.050666666666666665 ...\n", "Obs from Site B: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n", "Observed Prob_B: 0.04\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "LDzYsDVgMgsz" }, "cell_type": "markdown", "source": [ "Below we run inference over the new model:" ] }, { "metadata": { "colab_type": "code", "id": "7ghHBEdXYtxV", "colab": {} }, "cell_type": "code", "source": [ "def delta(prob_A, prob_B):\n", " \"\"\"\n", " Defining the deterministic delta function. This is our unknown of interest.\n", " \n", " Args:\n", " prob_A: scalar estimate of the probability of a 1 appearing in \n", " observation set A\n", " prob_B: scalar estimate of the probability of a 1 appearing in \n", " observation set B\n", " Returns: \n", " Difference between prob_A and prob_B\n", " \"\"\"\n", " return prob_A - prob_B\n", "\n", " \n", "def double_joint_log_prob(observations_A, observations_B, \n", " prob_A, prob_B):\n", " \"\"\"\n", " Joint log probability optimization function.\n", " \n", " Args:\n", " observations_A: An array of binary values representing the set of \n", " observations for site A\n", " observations_B: An array of binary values representing the set of \n", " observations for site B \n", " prob_A: scalar estimate of the probability of a 1 appearing in \n", " observation set A\n", " prob_B: scalar estimate of the probability of a 1 appearing in \n", " observation set B \n", " Returns: \n", " Joint log probability optimization function.\n", " \"\"\"\n", " tfd = tfp.distributions\n", " \n", " rv_prob_A = tfd.Uniform(low=0., high=1.)\n", " rv_prob_B = tfd.Uniform(low=0., high=1.)\n", " \n", " rv_obs_A = tfd.Bernoulli(probs=prob_A)\n", " rv_obs_B = tfd.Bernoulli(probs=prob_B)\n", " \n", " return (\n", " rv_prob_A.log_prob(prob_A)\n", " + rv_prob_B.log_prob(prob_B)\n", " + tf.reduce_sum(rv_obs_A.log_prob(observations_A))\n", " + tf.reduce_sum(rv_obs_B.log_prob(observations_B))\n", " )\n" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "code", "id": "h0TDeF3IIAyQ", "colab": {} }, "cell_type": "code", "source": [ "number_of_steps = 37200 #@param {type:\"slider\", min:2000, max:50000, step:100}\n", "#@markdown (Default is 18000).\n", "burnin = 1000 #@param {type:\"slider\", min:0, max:30000, step:100}\n", "#@markdown (Default is 1000).\n", "leapfrog_steps=3 #@param {type:\"slider\", min:1, max:9, step:1}\n", "#@markdown (Default is 6).\n", "\n", "\n", "# Set the chain's start state.\n", "initial_chain_state = [ \n", " tf.reduce_mean(tf.to_float(observations_A)) * tf.ones([], dtype=tf.float32, name=\"init_prob_A\"),\n", " tf.reduce_mean(tf.to_float(observations_B)) * tf.ones([], dtype=tf.float32, name=\"init_prob_B\")\n", "]\n", "\n", "# Since HMC operates over unconstrained space, we need to transform the\n", "# samples so they live in real-space.\n", "unconstraining_bijectors = [\n", " tfp.bijectors.Identity(), # Maps R to R.\n", " tfp.bijectors.Identity() # Maps R to R.\n", "]\n", "\n", "# Define a closure over our joint_log_prob.\n", "unnormalized_posterior_log_prob = lambda *args: double_joint_log_prob(observations_A, observations_B, *args)\n", "\n", "# Initialize the step_size. (It will be automatically adapted.)\n", "with tf.variable_scope(tf.get_variable_scope(), reuse=tf.AUTO_REUSE):\n", " step_size = tf.get_variable(\n", " name='step_size',\n", " initializer=tf.constant(0.5, dtype=tf.float32),\n", " trainable=False,\n", " use_resource=True\n", " )\n", "\n", "# Defining the HMC\n", "hmc=tfp.mcmc.TransformedTransitionKernel(\n", " inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(\n", " target_log_prob_fn=unnormalized_posterior_log_prob,\n", " num_leapfrog_steps=3,\n", " step_size=step_size,\n", " step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(num_adaptation_steps=int(burnin * 0.8)),\n", " state_gradients_are_stopped=True),\n", " bijector=unconstraining_bijectors)\n", "\n", "# Sample from the chain.\n", "[\n", " posterior_prob_A,\n", " posterior_prob_B\n", "], kernel_results = tfp.mcmc.sample_chain(\n", " num_results=number_of_steps,\n", " num_burnin_steps=burnin,\n", " current_state=initial_chain_state,\n", " kernel=hmc)\n", "\n", "# Initialize any created variables.\n", "init_g = tf.global_variables_initializer()\n", "init_l = tf.local_variables_initializer()" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "text", "id": "beUUmGMbdrRr" }, "cell_type": "markdown", "source": [ "#### Execute the TF graph to sample from the posterior" ] }, { "metadata": { "colab_type": "code", "id": "HTYITb9fdqIe", "outputId": "d91c2161-7644-4beb-9d17-66413ee86bf0", "colab": { "base_uri": "https://localhost:8080/", "height": 35 } }, "cell_type": "code", "source": [ "evaluate(init_g)\n", "evaluate(init_l)\n", "[\n", " posterior_prob_A_,\n", " posterior_prob_B_,\n", " kernel_results_\n", "] = evaluate([\n", " posterior_prob_A,\n", " posterior_prob_B,\n", " kernel_results\n", "])\n", " \n", "print(\"acceptance rate: {}\".format(\n", " kernel_results_.inner_results.is_accepted.mean()))\n", "\n", "burned_prob_A_trace_ = posterior_prob_A_[burnin:]\n", "burned_prob_B_trace_ = posterior_prob_B_[burnin:]\n", "burned_delta_trace_ = (posterior_prob_A_ - posterior_prob_B_)[burnin:]\n" ], "execution_count": 24, "outputs": [ { "output_type": "stream", "text": [ "acceptance rate: 0.6900537634408602\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "YaD67cOkIAyT" }, "cell_type": "markdown", "source": [ "Below we plot the posterior distributions for the three unknowns: " ] }, { "metadata": { "colab_type": "code", "id": "PpBXqVKELHRO", "outputId": "b7cfdf00-990c-416b-9b3f-9138eb77197e", "colab": { "base_uri": "https://localhost:8080/", "height": 908 } }, "cell_type": "code", "source": [ "plt.figure(figsize(12.5, 12.5))\n", "\n", "#histogram of posteriors\n", "\n", "ax = plt.subplot(311)\n", "\n", "plt.xlim(0, .1)\n", "plt.hist(burned_prob_A_trace_, histtype='stepfilled', bins=25, alpha=0.85,\n", " label=\"posterior of $p_A$\", color=TFColor[0], density=True)\n", "plt.vlines(true_prob_A_, 0, 80, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n", "plt.legend(loc=\"upper right\")\n", "plt.title(\"Posterior distributions of $p_A$, $p_B$, and delta unknowns\")\n", "\n", "ax = plt.subplot(312)\n", "\n", "plt.xlim(0, .1)\n", "plt.hist(burned_prob_B_trace_, histtype='stepfilled', bins=25, alpha=0.85,\n", " label=\"posterior of $p_B$\", color=TFColor[2], density=True)\n", "plt.vlines(true_prob_B_, 0, 80, linestyle=\"--\", label=\"true $p_B$ (unknown)\")\n", "plt.legend(loc=\"upper right\")\n", "\n", "ax = plt.subplot(313)\n", "plt.hist(burned_delta_trace_, histtype='stepfilled', bins=30, alpha=0.85,\n", " label=\"posterior of delta\", color=TFColor[6], density=True)\n", "plt.vlines(true_prob_A_ - true_prob_B_, 0, 60, linestyle=\"--\",\n", " label=\"true delta (unknown)\")\n", "plt.vlines(0, 0, 60, color=\"black\", alpha=0.2)\n", "plt.legend(loc=\"upper right\");" ], "execution_count": 25, "outputs": [ { "output_type": "stream", "text": [ "/usr/local/lib/python3.6/dist-packages/matplotlib/axes/_axes.py:6521: MatplotlibDeprecationWarning: \n", "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n", " alternative=\"'density'\", removal=\"3.1\")\n", "/usr/local/lib/python3.6/dist-packages/matplotlib/axes/_axes.py:6521: MatplotlibDeprecationWarning: \n", "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n", " alternative=\"'density'\", removal=\"3.1\")\n", "/usr/local/lib/python3.6/dist-packages/matplotlib/axes/_axes.py:6521: MatplotlibDeprecationWarning: \n", "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n", " alternative=\"'density'\", removal=\"3.1\")\n" ], "name": "stderr" }, { "output_type": "display_data", "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "tags": [], "image/png": { "width": 833, "height": 729 } } } ] }, { "metadata": { "colab_type": "text", "id": "Hn-G0eFwIAyh" }, "cell_type": "markdown", "source": [ "Notice that as a result of `N_B < N_A`, i.e. we have less data from site B, our posterior distribution of $p_B$ is fatter, implying we are less certain about the true value of $p_B$ than we are of $p_A$. \n", "\n", "With respect to the posterior distribution of $\\text{delta}$, we can see that the majority of the distribution is above $\\text{delta}=0$, implying there site A's response is likely better than site B's response. The probability this inference is incorrect is easily computable:" ] }, { "metadata": { "colab_type": "code", "id": "nZxDurxyIAyh", "outputId": "8515d96a-0c65-4843-a326-d39aa5bddea6", "colab": { "base_uri": "https://localhost:8080/", "height": 53 } }, "cell_type": "code", "source": [ "# Count the number of samples less than 0, i.e. the area under the curve\n", "# before 0, represent the probability that site A is worse than site B.\n", "print(\"Probability site A is WORSE than site B: %.3f\" % \\\n", " np.mean(burned_delta_trace_ < 0))\n", "\n", "print(\"Probability site A is BETTER than site B: %.3f\" % \\\n", " np.mean(burned_delta_trace_ > 0))" ], "execution_count": 26, "outputs": [ { "output_type": "stream", "text": [ "Probability site A is WORSE than site B: 0.294\n", "Probability site A is BETTER than site B: 0.706\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "Q8cAEzbUIAyl" }, "cell_type": "markdown", "source": [ "If this probability is too high for comfortable decision-making, we can perform more trials on site B (as site B has less samples to begin with, each additional data point for site B contributes more inferential \"power\" than each additional data point for site A). \n", "\n", "Try playing with the parameters `true_prob_A`, `true_prob_B`, `N_A`, and `N_B`, to see what the posterior of $\\text{delta}$ looks like. Notice in all this, the difference in sample sizes between site A and site B was never mentioned: it naturally fits into Bayesian analysis.\n", "\n", "I hope the readers feel this style of A/B testing is more natural than hypothesis testing, which has probably confused more than helped practitioners. Later in this book, we will see two extensions of this model: the first to help dynamically adjust for bad sites, and the second will improve the speed of this computation by reducing the analysis to a single equation. " ] }, { "metadata": { "colab_type": "text", "id": "f-jxOi70IAyl" }, "cell_type": "markdown", "source": [ "## An algorithm for human deceit\n", "\n", "Social data has an additional layer of interest as people are not always honest with responses, which adds a further complication into inference. For example, simply asking individuals \"Have you ever cheated on a test?\" will surely contain some rate of dishonesty. What you can say for certain is that the true rate is less than your observed rate (assuming individuals lie *only* about *not cheating*; I cannot imagine one who would admit \"Yes\" to cheating when in fact they hadn't cheated). \n", "\n", "To present an elegant solution to circumventing this dishonesty problem, and to demonstrate Bayesian modeling, we first need to introduce the binomial distribution.\n" ] }, { "metadata": { "colab_type": "text", "id": "qzCqZqzBDpMa" }, "cell_type": "markdown", "source": [ "## The Binomial Distribution\n", "\n", "The binomial distribution is one of the most popular distributions, mostly because of its simplicity and usefulness. Unlike the other distributions we have encountered thus far in the book, the binomial distribution has 2 parameters: $N$, a positive integer representing $N$ trials or number of instances of potential events, and $p$, the probability of an event occurring in a single trial. Like the Poisson distribution, it is a discrete distribution, but unlike the Poisson distribution, it only weighs integers from $0$ to $N$. The mass distribution looks like:\n", "\n", "$$P( X = k ) = {{N}\\choose{k}} p^k(1-p)^{N-k}$$\n", "\n", "If $X$ is a binomial random variable with parameters $p$ and $N$, denoted $X \\sim \\text{Bin}(N,p)$, then $X$ is the number of events that occurred in the $N$ trials (obviously $0 \\le X \\le N$). The larger $p$ is (while still remaining between 0 and 1), the more events are likely to occur. The expected value of a binomial is equal to $Np$. Below we plot the mass probability distribution for varying parameters. " ] }, { "metadata": { "colab_type": "code", "id": "9I53Ta3maWgJ", "outputId": "d1d4ea3c-9696-4e77-c821-9704c217c743", "colab": { "base_uri": "https://localhost:8080/", "height": 299 } }, "cell_type": "code", "source": [ "N = 10.\n", "k_values = tf.range(start=0, limit=(N + 1), dtype=tf.float32)\n", "rv_probs_1 = tfd.Binomial(total_count=N, probs=.4).prob(k_values)\n", "rv_probs_2 = tfd.Binomial(total_count=N, probs=.9).prob(k_values)\n", "\n", "# Execute graph\n", "[\n", " k_values_,\n", " rv_probs_1_,\n", " rv_probs_2_,\n", "] = evaluate([\n", " k_values,\n", " rv_probs_1,\n", " rv_probs_2,\n", "])\n", "\n", "# Display results\n", "plt.figure(figsize=(12.5, 4))\n", "colors = [TFColor[3], TFColor[0]] \n", "\n", "plt.bar(k_values_ - 0.5, rv_probs_1_, color=colors[0],\n", " edgecolor=colors[0],\n", " alpha=0.6,\n", " label=\"$N$: %d, $p$: %.1f\" % (10., .4),\n", " linewidth=3)\n", "plt.bar(k_values_ - 0.5, rv_probs_2_, color=colors[1],\n", " edgecolor=colors[1],\n", " alpha=0.6,\n", " label=\"$N$: %d, $p$: %.1f\" % (10., .9),\n", " linewidth=3)\n", "\n", "plt.legend(loc=\"upper left\")\n", "plt.xlim(0, 10.5)\n", "plt.xlabel(\"$k$\")\n", "plt.ylabel(\"$P(X = k)$\")\n", "plt.title(\"Probability mass distributions of binomial random variables\");" ], "execution_count": 27, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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Poi3I5ti5ETgoD9g3qmz1+Lzs6rG7XI+mlB4E9iGrOx/Py/1qnv8c4JCU0gs9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\ndee6dPUczzvvPA466CDOO++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" ] }, "metadata": { "tags": [], "image/png": { "width": 851, "height": 282 } } } ] }, { "metadata": { "id": "8qXPOubvsYht", "colab_type": "code", "colab": {} }, "cell_type": "code", "source": [ "" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "text", "id": "xT-q-ZI0IAys" }, "cell_type": "markdown", "source": [ "The special case when $N = 1$ corresponds to the Bernoulli distribution. There is another connection between Bernoulli and Binomial random variables. If we have $X_1, X_2, ... , X_N$ Bernoulli random variables with the same $p$, then $Z = X_1 + X_2 + ... + X_N \\sim \\text{Binomial}(N, p )$.\n", "\n", "The expected value of a Bernoulli random variable is $p$. This can be seen by noting the more general Binomial random variable has expected value $Np$ and setting $N=1$." ] }, { "metadata": { "colab_type": "text", "id": "9HmW-50PIAyv" }, "cell_type": "markdown", "source": [ "## Example: Cheating among students\n", "\n", "We will use the binomial distribution to determine the frequency of students cheating during an exam. If we let $N$ be the total number of students who took the exam, and assuming each student is interviewed post-exam (answering without consequence), we will receive integer $X$ \"Yes I did cheat\" answers. We then find the posterior distribution of $p$, given $N$, some specified prior on $p$, and observed data $X$. \n", "\n", "This is a completely absurd model. No student, even with a free-pass against punishment, would admit to cheating. What we need is a better *algorithm* to ask students if they had cheated. Ideally the algorithm should encourage individuals to be honest while preserving privacy. The following proposed algorithm is a solution I greatly admire for its ingenuity and effectiveness:\n", "\n", "> In the interview process for each student, the student flips a coin, hidden from the interviewer. The student agrees to answer honestly if the coin comes up heads. Otherwise, if the coin comes up tails, the student (secretly) flips the coin again, and answers \"Yes, I did cheat\" if the coin flip lands heads, and \"No, I did not cheat\", if the coin flip lands tails. This way, the interviewer does not know if a \"Yes\" was the result of a guilty plea, or a Heads on a second coin toss. Thus privacy is preserved and the researchers receive honest answers. \n", "\n", "I call this the Privacy Algorithm. One could of course argue that the interviewers are still receiving false data since some *Yes*'s are not confessions but instead randomness, but an alternative perspective is that the researchers are discarding approximately half of their original dataset since half of the responses will be noise. But they have gained a systematic data generation process that can be modeled. Furthermore, they do not have to incorporate (perhaps somewhat naively) the possibility of deceitful answers. We can use TFP to dig through this noisy model, and find a posterior distribution for the true frequency of liars. " ] }, { "metadata": { "colab_type": "text", "id": "gPcqaqxMIAyw" }, "cell_type": "markdown", "source": [ "Suppose 100 students are being surveyed for cheating, and we wish to find $p$, the proportion of cheaters. There are a few ways we can model this in TFP. I'll demonstrate the most explicit way, and later show a simplified version. Both versions arrive at the same inference. In our data-generation model, we sample $p$, the true proportion of cheaters, from a prior. Since we are quite ignorant about $p$, we will assign it a $\\text{Uniform}(0,1)$ prior." ] }, { "metadata": { "colab_type": "code", "id": "LIg-xs2LIAyw", "colab": {} }, "cell_type": "code", "source": [ "reset_sess()\n", "\n", "N = 100\n", "rv_p = tfd.Uniform(name=\"freq_cheating\", low=0., high=1.)" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "text", "id": "7L0nMGmrIAy0" }, "cell_type": "markdown", "source": [ "Again, thinking of our data-generation model, we assign Bernoulli random variables to the 100 students: 1 implies they cheated and 0 implies they did not. " ] }, { "metadata": { "colab_type": "code", "id": "aXxhrJdtIAy0", "outputId": "4c9363b3-9056-4500-8374-beba11e613ff", "colab": { "base_uri": "https://localhost:8080/", "height": 89 } }, "cell_type": "code", "source": [ "N = 100\n", "reset_sess()\n", "rv_p = tfd.Uniform(name=\"freq_cheating\", low=0., high=1.)\n", "true_answers = tfd.Bernoulli(name=\"truths\", \n", " probs=rv_p.sample()).sample(sample_shape=N, \n", " seed=5)\n", "# Execute graph\n", "[\n", " true_answers_,\n", "] = evaluate([\n", " true_answers,\n", "])\n", "\n", "print(true_answers_)\n", "print(true_answers_.sum())" ], "execution_count": 29, "outputs": [ { "output_type": "stream", "text": [ "[0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1\n", " 0 1 1 1 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0\n", " 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0]\n", "37\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "vNB9WGYcIAy4" }, "cell_type": "markdown", "source": [ "If we carry out the algorithm, the next step that occurs is the first coin-flip each student makes. This can be modeled again by sampling 100 Bernoulli random variables with $p=1/2$: denote a 1 as a *Heads* and 0 a *Tails*." ] }, { "metadata": { "colab_type": "code", "id": "68t8O39EIAy4", "outputId": "9d61b6b0-0a07-4859-ad85-056fcfe8b25e", "colab": { "base_uri": "https://localhost:8080/", "height": 71 } }, "cell_type": "code", "source": [ "N = 100\n", "first_coin_flips = tfd.Bernoulli(name=\"first_flips\", \n", " probs=0.5).sample(sample_shape=N, \n", " seed=5)\n", "# Execute graph\n", "[\n", " first_coin_flips_,\n", "] = evaluate([\n", " first_coin_flips,\n", "])\n", "\n", "print(first_coin_flips_)" ], "execution_count": 30, "outputs": [ { "output_type": "stream", "text": [ "[1 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1\n", " 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0\n", " 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1]\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "8-ZnScpWIAzA" }, "cell_type": "markdown", "source": [ "Although *not everyone* flips a second time, we can still model the possible realization of second coin-flips:" ] }, { "metadata": { "colab_type": "code", "id": "acP-4TAfIAzB", "outputId": "5a6909bc-9780-4185-fcd5-d3c7b0acbb1a", "colab": { "base_uri": "https://localhost:8080/", "height": 71 } }, "cell_type": "code", "source": [ "N = 100\n", "second_coin_flips = tfd.Bernoulli(name=\"second_flips\", \n", " probs=0.5).sample(sample_shape=N, \n", " seed=5)\n", "# Execute graph\n", "[\n", " second_coin_flips_,\n", "] = evaluate([\n", " second_coin_flips,\n", "])\n", "\n", "print(second_coin_flips_)" ], "execution_count": 31, "outputs": [ { "output_type": "stream", "text": [ "[1 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1\n", " 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0\n", " 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1]\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "uiVbAjoTIAzI" }, "cell_type": "markdown", "source": [ "Using these variables, we can return a possible realization of the *observed proportion* of \"Yes\" responses. " ] }, { "metadata": { "colab_type": "code", "id": "BJxN0jmBIAzJ", "colab": {} }, "cell_type": "code", "source": [ "def observed_proportion_calc(t_a = true_answers, \n", " fc = first_coin_flips,\n", " sc = second_coin_flips):\n", " \"\"\"\n", " Unnormalized log posterior distribution function\n", " \n", " Args:\n", " t_a: array of binary variables representing the true answers\n", " fc: array of binary variables representing the simulated first flips \n", " sc: array of binary variables representing the simulated second flips\n", " Returns: \n", " Observed proportion of coin flips\n", " Closure over: N\n", " \"\"\"\n", " observed = fc * t_a + (1 - fc) * sc\n", " observed_proportion = tf.to_float(tf.reduce_sum(observed)) / tf.to_float(N)\n", " \n", " return tf.to_float(observed_proportion)\n" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "text", "id": "OoIWHbsNIAzL" }, "cell_type": "markdown", "source": [ "The line `fc*t_a + (1-fc)*sc` contains the heart of the Privacy algorithm. Elements in this array are 1 *if and only if* i) the first toss is heads and the student cheated or ii) the first toss is tails, and the second is heads, and are 0 else. Finally, the last line sums this vector and divides by `float(N)`, producing a proportion. " ] }, { "metadata": { "colab_type": "code", "id": "ma5VwRSNIAzM", "outputId": "6e54ab97-f18a-4d5b-f373-31bda38b3e58", "colab": { "base_uri": "https://localhost:8080/", "height": 35 } }, "cell_type": "code", "source": [ "observed_proportion_val = observed_proportion_calc(t_a=true_answers_,\n", " fc=first_coin_flips_,\n", " sc=second_coin_flips_)\n", "# Execute graph\n", "[\n", " observed_proportion_val_,\n", "] = evaluate([\n", " observed_proportion_val,\n", "])\n", "\n", "print(observed_proportion_val_)" ], "execution_count": 33, "outputs": [ { "output_type": "stream", "text": [ "0.37\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "HNoBM39rIAzQ" }, "cell_type": "markdown", "source": [ "Next we need a dataset. After performing our coin-flipped interviews the researchers received 35 \"Yes\" responses. To put this into a relative perspective, if there truly were no cheaters, we should expect to see on average 1/4 of all responses being a \"Yes\" (half chance of having first coin land Tails, and another half chance of having second coin land Heads), so about 25 responses in a cheat-free world. On the other hand, if *all students cheated*, we should expected to see approximately 3/4 of all responses be \"Yes\". \n", "\n", "The researchers observe a Binomial random variable, with `N = 100` and `total_yes = 35`: " ] }, { "metadata": { "colab_type": "code", "id": "SLcH6ZPsIAzR", "colab": {} }, "cell_type": "code", "source": [ "total_count = 100\n", "total_yes = 35" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "code", "id": "-kWZd1ygofav", "colab": {} }, "cell_type": "code", "source": [ "def coin_joint_log_prob(total_yes, total_count, lies_prob):\n", " \"\"\"\n", " Joint log probability optimization function.\n", " \n", " Args:\n", " headsflips: Integer for total number of observed heads flips\n", " N: Integer for number of total observation\n", " lies_prob: Test probability of a heads flip (1) for a Binomial distribution\n", " Returns: \n", " Joint log probability optimization function.\n", " \"\"\"\n", " \n", " rv_lies_prob = tfd.Uniform(name=\"rv_lies_prob\",low=0., high=1.)\n", "\n", " cheated = tfd.Bernoulli(probs=tf.to_float(lies_prob)).sample(total_count)\n", " first_flips = tfd.Bernoulli(probs=0.5).sample(total_count)\n", " second_flips = tfd.Bernoulli(probs=0.5).sample(total_count)\n", " observed_probability = tf.reduce_sum(tf.to_float(\n", " cheated * first_flips + (1 - first_flips) * second_flips)) / total_count\n", "\n", " rv_yeses = tfd.Binomial(name=\"rv_yeses\",\n", " total_count=float(total_count),\n", " probs=observed_probability)\n", " \n", " return (\n", " rv_lies_prob.log_prob(lies_prob)\n", " + tf.reduce_sum(rv_yeses.log_prob(tf.to_float(total_yes)))\n", " )" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "text", "id": "QZC4TITlIAzV" }, "cell_type": "markdown", "source": [ "Below we add all the variables of interest to our Metropolis-Hastings sampler and run our black-box algorithm over the model. It's important to note that we're using a Metropolis-Hastings MCMC instead of a Hamiltonian since we're sampling inside." ] }, { "metadata": { "colab_type": "code", "id": "Awl3GmgjIAzV", "colab": {} }, "cell_type": "code", "source": [ "burnin = 15000\n", "num_of_steps = 40000\n", "total_count=100\n", "\n", "# Set the chain's start state.\n", "initial_chain_state = [\n", " 0.4 * tf.ones([], dtype=tf.float32, name=\"init_prob\")\n", "]\n", "\n", "# Define a closure over our joint_log_prob.\n", "unnormalized_posterior_log_prob = lambda *args: coin_joint_log_prob(total_yes, total_count, *args)\n", "\n", "# Defining the Metropolis-Hastings\n", "# We use a Metropolis-Hastings method here instead of Hamiltonian method\n", "# because the coin flips in the above example are non-differentiable and cannot\n", "# be used with HMC.\n", "metropolis=tfp.mcmc.RandomWalkMetropolis(\n", " target_log_prob_fn=unnormalized_posterior_log_prob,\n", " seed=54)\n", "\n", "# Sample from the chain.\n", "[\n", " posterior_p\n", "], kernel_results = tfp.mcmc.sample_chain(\n", " num_results=num_of_steps,\n", " num_burnin_steps=burnin,\n", " current_state=initial_chain_state,\n", " kernel=metropolis,\n", " parallel_iterations=1,\n", " name='Metropolis-Hastings_coin-flips')" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "text", "id": "Lq0OtJDCufOu" }, "cell_type": "markdown", "source": [ "##### Executing the TF graph to sample from the posterior" ] }, { "metadata": { "colab_type": "code", "id": "x--bCsBrr91E", "outputId": "3157cffc-ebd7-4588-fc37-4deeaab499ed", "colab": { "base_uri": "https://localhost:8080/", "height": 35 } }, "cell_type": "code", "source": [ "# Content Warning: This cell can take up to 5 minutes in Graph Mode\n", "[\n", " posterior_p_,\n", " kernel_results_\n", "] = evaluate([\n", " posterior_p,\n", " kernel_results,\n", "])\n", " \n", "print(\"acceptance rate: {}\".format(\n", " kernel_results_.is_accepted.mean()))\n", "# print(\"prob_p trace: \", posterior_p_)\n", "# print(\"prob_p burned trace: \", posterior_p_[burnin:])\n", "burned_cheating_freq_samples_ = posterior_p_[burnin:]" ], "execution_count": 37, "outputs": [ { "output_type": "stream", "text": [ "acceptance rate: 0.105425\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "QhCgk98ynq5s" }, "cell_type": "markdown", "source": [ "And finally we can plot the results." ] }, { "metadata": { "colab_type": "code", "id": "JoKNmLpxB1yt", "outputId": "f24aad88-b416-49bf-a883-53ac08022cbf", "colab": { "base_uri": "https://localhost:8080/", "height": 380 } }, "cell_type": "code", "source": [ "plt.figure(figsize(12.5, 6))\n", "p_trace_ = burned_cheating_freq_samples_\n", "plt.hist(p_trace_, histtype=\"stepfilled\", density=True, alpha=0.85, bins=30, \n", " label=\"posterior distribution\", color=TFColor[3])\n", "plt.vlines([.1, .40], [0, 0], [5, 5], alpha=0.3)\n", "plt.xlim(0, 1)\n", "plt.legend();" ], "execution_count": 38, "outputs": [ { "output_type": 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" ] }, "metadata": { "tags": [], "image/png": { "width": 822, "height": 363 } } } ] }, { "metadata": { "colab_type": "text", "id": "tqDMt8xyIAzd" }, "cell_type": "markdown", "source": [ "With regards to the above plot, we are still pretty uncertain about what the true frequency of cheaters might be, but we have narrowed it down to a range between 0.1 to 0.4 (marked by the solid lines). This is pretty good, as *a priori* we had no idea how many students might have cheated (hence the uniform distribution for our prior). On the other hand, it is also pretty bad since there is a .3 length window the true value most likely lives in. Have we even gained anything, or are we still too uncertain about the true frequency? \n", "\n", "I would argue, yes, we have discovered something. It is implausible, according to our posterior, that there are *no cheaters*, i.e. the posterior assigns low probability to $p=0$. Since we started with an uniform prior, treating all values of $p$ as equally plausible, but the data ruled out $p=0$ as a possibility, we can be confident that there were cheaters. \n", "\n", "This kind of algorithm can be used to gather private information from users and be *reasonably* confident that the data, though noisy, is truthful. \n", "\n" ] }, { "metadata": { "colab_type": "text", "id": "Y0bK5tMAIAze" }, "cell_type": "markdown", "source": [ "### Alternative TFP Model\n", "\n", "Given a value for $p$ (which from our god-like position we know), we can find the probability the student will answer yes: \n", "$$\n", "\\begin{align}\n", "P(\\text{\"Yes\"}) &= P( \\text{Heads on first coin} )P( \\text{cheater} ) + P( \\text{Tails on first coin} )P( \\text{Heads on second coin} ) \\\\\n", "&= \\frac{1}{2}p + \\frac{1}{2}\\frac{1}{2}\\\\\n", "&= \\frac{p}{2} + \\frac{1}{4}\n", "\\end{align}\n", "$$\n", "Thus, knowing $p$ we know the probability a student will respond \"Yes\". " ] }, { "metadata": { "colab_type": "text", "id": "m_kgk64TIAzh" }, "cell_type": "markdown", "source": [ "If we know the probability of respondents saying \"Yes\", which is `p_skewed`, and we have $N=100$ students, the number of \"Yes\" responses is a binomial random variable with parameters `N` and `p_skewed`.\n", "\n", "This is where we include our observed 35 \"Yes\" responses out of a total of 100, which are then passed to the `joint_log_prob` in the code section further below, where we define our closure over the`joint_log_prob`." ] }, { "metadata": { "colab_type": "code", "id": "GJ2jFKI7ofa9", "colab": {} }, "cell_type": "code", "source": [ "N = 100.\n", "total_yes = 35.\n", "\n", "def alt_joint_log_prob(yes_responses, N, prob_cheating):\n", " \"\"\"\n", " Alternative joint log probability optimization function.\n", " \n", " Args:\n", " yes_responses: Integer for total number of affirmative responses\n", " N: Integer for number of total observation\n", " prob_cheating: Test probability of a student actually cheating\n", " Returns: \n", " Joint log probability optimization function.\n", " \"\"\"\n", " tfd = tfp.distributions\n", " \n", " rv_prob = tfd.Uniform(name=\"rv_prob\", low=0., high=1.)\n", " p_skewed = 0.5 * prob_cheating + 0.25\n", " rv_yes_responses = tfd.Binomial(name=\"rv_yes_responses\",\n", " total_count=tf.to_float(N), \n", " probs=p_skewed)\n", "\n", " return (\n", " rv_prob.log_prob(prob_cheating)\n", " + tf.reduce_sum(rv_yes_responses.log_prob(tf.to_float(yes_responses)))\n", " )" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "text", "id": "0clIAcyHIAzj" }, "cell_type": "markdown", "source": [ "\n", "Below we add all the variables of interest to our HMC component-defining cell and run our black-box algorithm over the model. " ] }, { "metadata": { "colab_type": "code", "id": "C5QLZ17e5u6t", "colab": {} }, "cell_type": "code", "source": [ "number_of_steps = 25000\n", "burnin = 2500\n", "\n", "# Set the chain's start state.\n", "initial_chain_state = [\n", " 0.2 * tf.ones([], dtype=tf.float32, name=\"init_skewed_p\")\n", "]\n", "\n", "# Since HMC operates over unconstrained space, we need to transform the\n", "# samples so they live in real-space.\n", "unconstraining_bijectors = [\n", " tfp.bijectors.Sigmoid(), # Maps [0,1] to R.\n", "]\n", "\n", "# Define a closure over our joint_log_prob.\n", "# unnormalized_posterior_log_prob = lambda *args: alt_joint_log_prob(headsflips, total_yes, N, *args)\n", "unnormalized_posterior_log_prob = lambda *args: alt_joint_log_prob(total_yes, N, *args)\n", "\n", "# Initialize the step_size. (It will be automatically adapted.)\n", "with tf.variable_scope(tf.get_variable_scope(), reuse=tf.AUTO_REUSE):\n", " step_size = tf.get_variable(\n", " name='skewed_step_size',\n", " initializer=tf.constant(0.5, dtype=tf.float32),\n", " trainable=False,\n", " use_resource=True\n", " ) \n", "\n", "# Defining the HMC\n", "hmc=tfp.mcmc.TransformedTransitionKernel(\n", " inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(\n", " target_log_prob_fn=unnormalized_posterior_log_prob,\n", " num_leapfrog_steps=2,\n", " step_size=step_size,\n", " step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(num_adaptation_steps=int(burnin * 0.8)),\n", " state_gradients_are_stopped=True),\n", " bijector=unconstraining_bijectors)\n", "\n", "# Sample from the chain.\n", "[\n", " posterior_skewed_p\n", "], kernel_results = tfp.mcmc.sample_chain(\n", " num_results=number_of_steps,\n", " num_burnin_steps=burnin,\n", " current_state=initial_chain_state,\n", " kernel=hmc)\n", "\n", "# Initialize any created variables.\n", "# This prevents a FailedPreconditionError\n", "init_g = tf.global_variables_initializer()\n", "init_l = tf.local_variables_initializer()" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "text", "id": "eJYLS8EysHqj" }, "cell_type": "markdown", "source": [ "#### Execute the TF graph to sample from the posterior" ] }, { "metadata": { "colab_type": "code", "id": "ALvEN1yQkTIx", "colab": { "base_uri": "https://localhost:8080/", "height": 35 }, "outputId": "b20176e2-3b33-4654-e82a-9cb2c44c7e47" }, "cell_type": "code", "source": [ "# This cell may take 5 minutes in Graph Mode\n", "evaluate(init_g)\n", "evaluate(init_l)\n", "[\n", " posterior_skewed_p_,\n", " kernel_results_\n", "] = evaluate([\n", " posterior_skewed_p,\n", " kernel_results\n", "])\n", "\n", " \n", "print(\"acceptance rate: {}\".format(\n", " kernel_results_.inner_results.is_accepted.mean()))\n", "# print(\"final step size: {}\".format(\n", "# kernel_results_.inner_results.extra.step_size_assign[-100:].mean()))\n", "\n", "# print(\"p_skewed trace: \", posterior_skewed_p_)\n", "# print(\"p_skewed burned trace: \", posterior_skewed_p_[burnin:])\n", "freq_cheating_samples_ = posterior_skewed_p_[burnin:]\n" ], "execution_count": 42, "outputs": [ { "output_type": "stream", "text": [ "acceptance rate: 0.56236\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "Ye0uC_c-xrWf" }, "cell_type": "markdown", "source": [ "Now we can plot our results" ] }, { "metadata": { "colab_type": "code", "id": "_P5Z_uySgi-S", "colab": { "base_uri": "https://localhost:8080/", "height": 434 }, "outputId": "d45b8c22-40b1-4477-d5e7-34020ca316ce" }, "cell_type": "code", "source": [ "plt.figure(figsize(12.5, 6))\n", "p_trace_ = freq_cheating_samples_\n", "plt.hist(p_trace_, histtype=\"stepfilled\", density=True, alpha=0.85, bins=30, \n", " label=\"posterior distribution\", color=TFColor[3])\n", "plt.vlines([.1, .40], [0, 0], [5, 5], alpha=0.2)\n", "plt.xlim(0, 1)\n", "plt.legend();" ], "execution_count": 43, "outputs": [ { "output_type": "stream", "text": [ "/usr/local/lib/python3.6/dist-packages/matplotlib/axes/_axes.py:6521: MatplotlibDeprecationWarning: \n", "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n", " alternative=\"'density'\", removal=\"3.1\")\n" ], "name": "stderr" }, { "output_type": "display_data", "data": { "image/png": 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" ] }, "metadata": { "tags": [], "image/png": { "width": 822, "height": 363 } } } ] }, { "metadata": { "colab_type": "text", "id": "Lxt6fSRvIAzy" }, "cell_type": "markdown", "source": [ "The remainder of this chapter examines some practical examples of TFP and TFP modeling:" ] }, { "metadata": { "colab_type": "text", "id": "KMoiodMmIAzy" }, "cell_type": "markdown", "source": [ "## Example: Challenger Space Shuttle Disaster \n", "\n", "On January 28, 1986, the twenty-fifth flight of the U.S. space shuttle program ended in disaster when one of the rocket boosters of the Shuttle Challenger exploded shortly after lift-off, killing all seven crew members. The presidential commission on the accident concluded that it was caused by the failure of an O-ring in a field joint on the rocket booster, and that this failure was due to a faulty design that made the O-ring unacceptably sensitive to a number of factors including outside temperature. Of the previous 24 flights, data were available on failures of O-rings on 23, (one was lost at sea), and these data were discussed on the evening preceding the Challenger launch, but unfortunately only the data corresponding to the 7 flights on which there was a damage incident were considered important and these were thought to show no obvious trend. The data are shown below (see [1]):\n", "\n", "\n", "\n", "\n" ] }, { "metadata": { "colab_type": "code", "id": "tlPZvBWkg5g-", "outputId": "98b6c9e2-3959-4245-bc38-787c2b91700e", "colab": { "base_uri": "https://localhost:8080/", "height": 35 } }, "cell_type": "code", "source": [ "reset_sess()\n", "\n", "import wget\n", "url = 'https://raw.githubusercontent.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter2_MorePyMC/data/challenger_data.csv'\n", "filename = wget.download(url)\n", "filename" ], "execution_count": 44, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "'challenger_data.csv'" ] }, "metadata": { "tags": [] }, "execution_count": 44 } ] }, { "metadata": { "colab_type": "code", "id": "BNOqG_9zIAzz", "outputId": "45b8f986-7cd6-4c44-e919-73a7c5bd08fa", "colab": { "base_uri": "https://localhost:8080/", "height": 704 } }, "cell_type": "code", "source": [ "plt.figure(figsize(12.5, 3.5))\n", "np.set_printoptions(precision=3, suppress=True)\n", "challenger_data_ = np.genfromtxt(\"challenger_data.csv\", skip_header=1,\n", " usecols=[1, 2], missing_values=\"NA\",\n", " delimiter=\",\")\n", "#drop the NA values\n", "challenger_data_ = challenger_data_[~np.isnan(challenger_data_[:, 1])]\n", "\n", "#plot it, as a function of tempature (the first column)\n", "print(\"Temp (F), O-Ring failure?\")\n", "print(challenger_data_)\n", "\n", "plt.scatter(challenger_data_[:, 0], challenger_data_[:, 1], s=75, color=\"k\",\n", " alpha=0.5)\n", "plt.yticks([0, 1])\n", "plt.ylabel(\"Damage Incident?\")\n", "plt.xlabel(\"Outside temperature (Fahrenheit)\")\n", "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\");\n" ], "execution_count": 45, "outputs": [ { "output_type": "stream", "text": [ "Temp (F), O-Ring failure?\n", "[[66. 0.]\n", " [70. 1.]\n", " [69. 0.]\n", " [68. 0.]\n", " [67. 0.]\n", " [72. 0.]\n", " [73. 0.]\n", " [70. 0.]\n", " [57. 1.]\n", " [63. 1.]\n", " [70. 1.]\n", " [78. 0.]\n", " [67. 0.]\n", " [53. 1.]\n", " [67. 0.]\n", " [75. 0.]\n", " [70. 0.]\n", " [81. 0.]\n", " [76. 0.]\n", " [79. 0.]\n", " [75. 1.]\n", " [76. 0.]\n", " [58. 1.]]\n" ], "name": "stdout" }, { "output_type": "display_data", "data": { "image/png": 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qIZNAkiRJkiRJkiRJNWQSSJIkSZIkSZIkqYZM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\ndevVwBmjHYfUqVtuuQWAk046aZQjkXSo2O+liWe89vstW7Z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" ] }, "metadata": { "tags": [], "image/png": { "width": 832, "height": 255 } } } ] }, { "metadata": { "colab_type": "text", "id": "El9Z_4ulIAz3" }, "cell_type": "markdown", "source": [ "It looks clear that *the probability* of damage incidents occurring increases as the outside temperature decreases. We are interested in modeling the probability here because it does not look like there is a strict cutoff point between temperature and a damage incident occurring. The best we can do is ask \"At temperature $t$, what is the probability of a damage incident?\". The goal of this example is to answer that question.\n", "\n", "We need a function of temperature, call it $p(t)$, that is bounded between 0 and 1 (so as to model a probability) and changes from 1 to 0 as we increase temperature. There are actually many such functions, but the most popular choice is the *logistic function.*\n", "\n", "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t } } $$\n", "\n", "In this model, $\\beta$ is the variable we are uncertain about. Below is the function plotted for $\\beta = 1, 3, -5$." ] }, { "metadata": { "colab_type": "code", "id": "U4kW2QIddYEs", "outputId": "6decde20-489e-4bb0-a52d-0aabaa05a131", "colab": { "base_uri": "https://localhost:8080/", "height": 216 } }, "cell_type": "code", "source": [ "def logistic(x, beta):\n", " \"\"\"\n", " Logistic Function\n", " \n", " Args:\n", " x: independent variable\n", " beta: beta term\n", " Returns: \n", " Logistic function\n", " \"\"\"\n", " return 1.0 / (1.0 + tf.exp(beta * x))\n", "\n", "x_vals = tf.linspace(start=-4., stop=4., num=100)\n", "log_beta_1 = logistic(x_vals, 1.)\n", "log_beta_3 = logistic(x_vals, 3.)\n", "log_beta_m5 = logistic(x_vals, -5.)\n", "\n", "[\n", " x_vals_,\n", " log_beta_1_,\n", " log_beta_3_,\n", " log_beta_m5_,\n", "] = evaluate([\n", " x_vals,\n", " log_beta_1,\n", " log_beta_3,\n", " log_beta_m5,\n", "])\n", "\n", "plt.figure(figsize(12.5, 3))\n", "plt.plot(x_vals_, log_beta_1_, label=r\"$\\beta = 1$\", color=TFColor[0])\n", "plt.plot(x_vals_, log_beta_3_, label=r\"$\\beta = 3$\", color=TFColor[3])\n", "plt.plot(x_vals_, log_beta_m5_, label=r\"$\\beta = -5$\", color=TFColor[6])\n", "plt.legend();" ], "execution_count": 46, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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oAp+mJlizBtY0wYqVGukjssB4PYb9TSHuWxPkbH+Gn7QnONU7MbXj+YEM5weG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\nsFeaK3cGvTIL1kLOQ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" ] }, "metadata": { "tags": [], "image/png": { "width": 827, "height": 199 } } } ] }, { "metadata": { "colab_type": "text", "id": "H_rdEcFIIAz7" }, "cell_type": "markdown", "source": [ "But something is missing. In the plot of the logistic function, the probability changes only near zero, but in our data above the probability changes around 65 to 70. We need to add a *bias* term to our logistic function:\n", "\n", "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t + \\alpha } } $$\n", "\n", "Some plots are below, with differing $\\alpha$." ] }, { "metadata": { "colab_type": "code", "id": "T0iZj_eCIAz8", "outputId": "007ec106-e0af-421b-fa6b-0aaa21a09f9c", "colab": { "base_uri": "https://localhost:8080/", "height": 216 } }, "cell_type": "code", "source": [ "def logistic(x, beta, alpha=0):\n", " \"\"\"\n", " Logistic Function with offset\n", " \n", " Args:\n", " x: independent variable\n", " beta: beta term \n", " alpha: alpha term\n", " Returns: \n", " Logistic function\n", " \"\"\"\n", " return 1.0 / (1.0 + tf.exp((beta * x) + alpha))\n", "\n", "x_vals = tf.linspace(start=-4., stop=4., num=100)\n", "log_beta_1_alpha_1 = logistic(x_vals, 1, 1)\n", "log_beta_3_alpha_m2 = logistic(x_vals, 3, -2)\n", "log_beta_m5_alpha_7 = logistic(x_vals, -5, 7)\n", "\n", "[\n", " x_vals_,\n", " log_beta_1_alpha_1_,\n", " log_beta_3_alpha_m2_,\n", " log_beta_m5_alpha_7_,\n", "] = evaluate([\n", " x_vals,\n", " log_beta_1_alpha_1,\n", " log_beta_3_alpha_m2,\n", " log_beta_m5_alpha_7,\n", "])\n", "\n", "plt.figure(figsize(12.5, 3))\n", "plt.plot(x_vals_, log_beta_1_, label=r\"$\\beta = 1$\", ls=\"--\", lw=1, color=TFColor[0])\n", "plt.plot(x_vals_, log_beta_3_, label=r\"$\\beta = 3$\", ls=\"--\", lw=1, color=TFColor[3])\n", "plt.plot(x_vals_, log_beta_m5_, label=r\"$\\beta = -5$\", ls=\"--\", lw=1, color=TFColor[6])\n", "plt.plot(x_vals_, log_beta_1_alpha_1_, label=r\"$\\beta = 1, \\alpha = 1$\", color=TFColor[0])\n", "plt.plot(x_vals_, log_beta_3_alpha_m2_, label=r\"$\\beta = 3, \\alpha = -2$\", color=TFColor[3])\n", "plt.plot(x_vals_, log_beta_m5_alpha_7_, label=r\"$\\beta = -5, \\alpha = 7$\", color=TFColor[6])\n", "plt.legend(loc=\"lower left\");" ], "execution_count": 47, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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Jt2cE+Pf/qXS31MIok1FhULSsb+83PgC5d59al83a84yaF1vtAEA2CylERUhU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\n6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Mvy4GlStSOEEEKI3keSO6Jbbdu2jcWLFzN+/HjCwsKIiopi9uzZvPjii/1mAOmSJUsI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\nej1CY8Tw11d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" ] }, "metadata": { "tags": [], "image/png": { "width": 827, "height": 199 } } } ] }, { "metadata": { "colab_type": "text", "id": "W_B8n8wuIAz9" }, "cell_type": "markdown", "source": [ "Adding a constant term $\\alpha$ amounts to shifting the curve left or right (hence why it is called a *bias*).\n", "\n", "Let's start modeling this in TFP. The $\\beta, \\alpha$ parameters have no reason to be positive, bounded or relatively large, so they are best modeled by a *Normal random variable*, introduced next." ] }, { "metadata": { "colab_type": "text", "id": "_52Ml-KhIAz9" }, "cell_type": "markdown", "source": [ "### Normal distributions\n", "\n", "A Normal random variable, denoted $X \\sim N(\\mu, 1/\\tau)$, has a distribution with two parameters: the mean, $\\mu$, and the *precision*, $\\tau$. Those familiar with the Normal distribution already have probably seen $\\sigma^2$ instead of $\\tau^{-1}$. They are in fact reciprocals of each other. The change was motivated by simpler mathematical analysis and is an artifact of older Bayesian methods. Just remember: the smaller $\\tau$, the larger the spread of the distribution (i.e. we are more uncertain); the larger $\\tau$, the tighter the distribution (i.e. we are more certain). Regardless, $\\tau$ is always positive. \n", "\n", "The probability density function of a $N( \\mu, 1/\\tau)$ random variable is:\n", "\n", "$$ f(x | \\mu, \\tau) = \\sqrt{\\frac{\\tau}{2\\pi}} \\exp\\left( -\\frac{\\tau}{2} (x-\\mu)^2 \\right) $$\n", "\n", "We plot some different density functions below. " ] }, { "metadata": { "colab_type": "code", "id": "OLw3-8x2hxkm", "outputId": "1f92bc9f-589c-4764-fa41-695b0e81270c", "colab": { "base_uri": "https://localhost:8080/", "height": 245 } }, "cell_type": "code", "source": [ "rand_x_vals = tf.linspace(start=-8., stop=7., num=150)\n", "\n", "density_func_1 = tfd.Normal(loc=float(-2.), scale=float(1./.7)).prob(rand_x_vals)\n", "density_func_2 = tfd.Normal(loc=float(0.), scale=float(1./1)).prob(rand_x_vals)\n", "density_func_3 = tfd.Normal(loc=float(3.), scale=float(1./2.8)).prob(rand_x_vals)\n", "\n", "[\n", " rand_x_vals_,\n", " density_func_1_,\n", " density_func_2_,\n", " density_func_3_,\n", "] = evaluate([\n", " rand_x_vals,\n", " density_func_1,\n", " density_func_2,\n", " density_func_3,\n", "])\n", "\n", "colors = [TFColor[3], TFColor[0], TFColor[6]]\n", "\n", "plt.figure(figsize(12.5, 3))\n", "plt.plot(rand_x_vals_, density_func_1_,\n", " label=r\"$\\mu = %d, \\tau = %.1f$\" % (-2., .7), color=TFColor[3])\n", "plt.fill_between(rand_x_vals_, density_func_1_, color=TFColor[3], alpha=.33)\n", "plt.plot(rand_x_vals_, density_func_2_, \n", " label=r\"$\\mu = %d, \\tau = %.1f$\" % (0., 1), color=TFColor[0])\n", "plt.fill_between(rand_x_vals_, density_func_2_, color=TFColor[0], alpha=.33)\n", "plt.plot(rand_x_vals_, density_func_3_,\n", " label=r\"$\\mu = %d, \\tau = %.1f$\" % (3., 2.8), color=TFColor[6])\n", "plt.fill_between(rand_x_vals_, density_func_3_, color=TFColor[6], alpha=.33)\n", "\n", "plt.legend(loc=r\"upper right\")\n", "plt.xlabel(r\"$x$\")\n", "plt.ylabel(r\"density function at $x$\")\n", "plt.title(r\"Probability distribution of three different Normal random variables\");" ], "execution_count": 48, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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CdprZ3uAz8x7wJL6FRNYEwddHg7eLzKwm6jN+abJ108znL/jrc7I0rcBngC34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\niKcDT19P2+uvv/6KK664gunpaQ4fPryet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" ] }, "metadata": { "tags": [], "image/png": { "width": 845, "height": 228 } } } ] }, { "metadata": { "colab_type": "text", "id": "HAxWLKGcIA0A" }, "cell_type": "markdown", "source": [ "A Normal random variable can be take on any real number, but the variable is very likely to be relatively close to $\\mu$. In fact, the expected value of a Normal is equal to its $\\mu$ parameter:\n", "\n", "$$ E[ X | \\mu, \\tau] = \\mu$$\n", "\n", "and its variance is equal to the inverse of $\\tau$:\n", "\n", "$$\\text{Var}( X | \\mu, \\tau ) = \\frac{1}{\\tau}$$\n", "\n", "\n", "\n", "Below we continue our modeling of the Challenger space craft:" ] }, { "metadata": { "colab_type": "code", "id": "F3DBYxvAIA0B", "colab": {} }, "cell_type": "code", "source": [ "reset_sess()\n", "\n", "temperature_ = challenger_data_[:, 0]\n", "temperature = tf.convert_to_tensor(temperature_, dtype=tf.float32)\n", "D_ = challenger_data_[:, 1] # defect or not?\n", "D = tf.convert_to_tensor(D_, dtype=tf.float32)\n", "\n", "beta = tfd.Normal(name=\"beta\", loc=0.3, scale=1000.).sample()\n", "alpha = tfd.Normal(name=\"alpha\", loc=-15., scale=1000.).sample()\n", "p_deterministic = tfd.Deterministic(name=\"p\", loc=1.0/(1. + tf.exp(beta * temperature_ + alpha))).sample()\n", "\n", "[\n", " prior_alpha_,\n", " prior_beta_,\n", " p_deterministic_,\n", " D_,\n", "] = evaluate([\n", " alpha,\n", " beta,\n", " p_deterministic,\n", " D,\n", "])\n" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "text", "id": "PxOWy25CIA0D" }, "cell_type": "markdown", "source": [ "We have our probabilities, but how do we connect them to our observed data? A *Bernoulli* random variable with parameter $p$, denoted $\\text{Ber}(p)$, is a random variable that takes value 1 with probability $p$, and 0 else. Thus, our model can look like:\n", "\n", "$$ \\text{Defect Incident, }D_i \\sim \\text{Ber}( \\;p(t_i)\\; ), \\;\\; i=1..N$$\n", "\n", "where $p(t)$ is our logistic function and $t_i$ are the temperatures we have observations about. Notice in the code below we set the values of `beta` and `alpha` to 0 in `initial_chain_state`. The reason for this is that if `beta` and `alpha` are very large, they make `p` equal to 1 or 0. Unfortunately, `tfd.Bernoulli` does not like probabilities of exactly 0 or 1, though they are mathematically well-defined probabilities. So, by setting the coefficient values to `0`, we set the variable `p` to be a reasonable starting value. This has no effect on our results, nor does it mean we are including any additional information in our prior. It is simply a computational caveat in TFP. " ] }, { "metadata": { "colab_type": "code", "id": "vRqoyxqnofbT", "colab": {} }, "cell_type": "code", "source": [ "def challenger_joint_log_prob(D, temperature_, alpha, beta):\n", " \"\"\"\n", " Joint log probability optimization function.\n", " \n", " Args:\n", " D: The Data from the challenger disaster representing presence or \n", " absence of defect\n", " temperature_: The Data from the challenger disaster, specifically the temperature on \n", " the days of the observation of the presence or absence of a defect\n", " alpha: one of the inputs of the HMC\n", " beta: one of the inputs of the HMC\n", " Returns: \n", " Joint log probability optimization function.\n", " \"\"\"\n", " rv_alpha = tfd.Normal(loc=0., scale=1000.)\n", " rv_beta = tfd.Normal(loc=0., scale=1000.)\n", "\n", " # make this into a logit\n", " logistic_p = 1.0/(1. + tf.exp(beta * tf.to_float(temperature_) + alpha))\n", " rv_observed = tfd.Bernoulli(probs=logistic_p)\n", " \n", " return (\n", " rv_alpha.log_prob(alpha)\n", " + rv_beta.log_prob(beta)\n", " + tf.reduce_sum(rv_observed.log_prob(D))\n", " )" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "code", "id": "oHU-MbPxs8iL", "cellView": "code", "colab": {} }, "cell_type": "code", "source": [ "number_of_steps = 10000 #@param {type:\"slider\", min:2500, max:120000, step:100}\n", "burnin = 2000 #@param {type:\"slider\", min:2000, max:100000, step:100}\n", "\n", "# Set the chain's start state.\n", "initial_chain_state = [\n", " 0. * tf.ones([], dtype=tf.float32, name=\"init_alpha\"),\n", " 0. * tf.ones([], dtype=tf.float32, name=\"init_beta\")\n", "]\n", "\n", "# Since HMC operates over unconstrained space, we need to transform the\n", "# samples so they live in real-space.\n", "# Alpha is 100x of beta approximately, so apply Affine scalar bijector\n", "# to multiply the unconstrained alpha by 100 to get back to \n", "# the Challenger problem space\n", "unconstraining_bijectors = [\n", " tfp.bijectors.AffineScalar(100.),\n", " tfp.bijectors.Identity()\n", "]\n", "\n", "# Define a closure over our joint_log_prob.\n", "unnormalized_posterior_log_prob = lambda *args: challenger_joint_log_prob(D, temperature_, *args)\n", "\n", "# Initialize the step_size. (It will be automatically adapted.)\n", "with tf.variable_scope(tf.get_variable_scope(), reuse=tf.AUTO_REUSE):\n", " step_size = tf.get_variable(\n", " name='step_size',\n", " initializer=tf.constant(0.01, dtype=tf.float32),\n", " trainable=False,\n", " use_resource=True\n", " )\n", "\n", "# Defining the HMC\n", "hmc=tfp.mcmc.TransformedTransitionKernel(\n", " inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(\n", " target_log_prob_fn=unnormalized_posterior_log_prob,\n", " num_leapfrog_steps=40, #to improve convergence\n", " step_size=step_size,\n", " step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(\n", " num_adaptation_steps=int(burnin * 0.8)),\n", " state_gradients_are_stopped=True),\n", " bijector=unconstraining_bijectors)\n", "\n", "# Sampling from the chain.\n", "[\n", " posterior_alpha,\n", " posterior_beta\n", "], kernel_results = tfp.mcmc.sample_chain(\n", " num_results = number_of_steps,\n", " num_burnin_steps = burnin,\n", " current_state=initial_chain_state,\n", " kernel=hmc)\n", "\n", "## Initialize any created variables for preconditions\n", "init_g = tf.global_variables_initializer()" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "text", "id": "eNkhSXDkthRs" }, "cell_type": "markdown", "source": [ "#### Execute the TF graph to sample from the posterior" ] }, { "metadata": { "colab_type": "code", "id": "XJyZIwoyth2j", "outputId": "4debdde9-d4eb-41af-f59f-335ba214f5af", "colab": { "base_uri": "https://localhost:8080/", "height": 89 } }, "cell_type": "code", "source": [ "%%time\n", "# In Graph Mode, this cell can take up to 15 Minutes\n", "evaluate(init_g)\n", "[\n", " posterior_alpha_,\n", " posterior_beta_,\n", " kernel_results_\n", "] = evaluate([\n", " posterior_alpha,\n", " posterior_beta,\n", " kernel_results\n", "])\n", " \n", "print(\"acceptance rate: {}\".format(\n", " kernel_results_.inner_results.is_accepted.mean()))\n", "print(\"final step size: {}\".format(\n", " kernel_results_.inner_results.extra.step_size_assign[-100:].mean()))\n" ], "execution_count": 52, "outputs": [ { "output_type": "stream", "text": [ "acceptance rate: 0.7445\n", "final step size: 0.01269734837114811\n", "CPU times: user 19min 6s, sys: 2min 18s, total: 21min 24s\n", "Wall time: 12min 28s\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "xIGyBkilIA0G" }, "cell_type": "markdown", "source": [ "We have trained our model on the observed data, so lets look at the posterior distributions for $\\alpha$ and $\\beta$:" ] }, { "metadata": { "colab_type": "code", "id": "Pdgjgw9RiluO", "outputId": "0bc1e51c-d0ad-444e-920f-9cfc293d35df", "colab": { "base_uri": "https://localhost:8080/", "height": 393 } }, "cell_type": "code", "source": [ "plt.figure(figsize(12.5, 6))\n", "\n", "#histogram of the samples:\n", "plt.subplot(211)\n", "plt.title(r\"Posterior distributions of the variables $\\alpha, \\beta$\")\n", "plt.hist(posterior_beta_, histtype='stepfilled', bins=35, alpha=0.85,\n", " label=r\"posterior of $\\beta$\", color=TFColor[6], density=True)\n", "plt.legend()\n", "\n", "plt.subplot(212)\n", "plt.hist(posterior_alpha_, histtype='stepfilled', bins=35, alpha=0.85,\n", " label=r\"posterior of $\\alpha$\", color=TFColor[0], density=True)\n", "plt.legend();" ], "execution_count": 53, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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5HHHEEey6667sueeefOQjH+HJJ5/s8LznnnuO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\norGGGKOBbwDZlWtLkiRJkiRJkiQNNoUUhSLiBOBM4EXgrZk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"text/plain": [ "
" ] }, "metadata": { "tags": [], "image/png": { "width": 834, "height": 376 } } } ] }, { "metadata": { "colab_type": "text", "id": "gp0QmuZvIA0L" }, "cell_type": "markdown", "source": [ "All samples of $\\beta$ are greater than 0. If instead the posterior was centered around 0, we may suspect that $\\beta = 0$, implying that temperature has no effect on the probability of defect. \n", "\n", "Similarly, all $\\alpha$ posterior values are negative and far away from 0, implying that it is correct to believe that $\\alpha$ is significantly less than 0. \n", "\n", "Regarding the spread of the data, we are very uncertain about what the true parameters might be (though considering the low sample size and the large overlap of defects-to-nondefects this behaviour is perhaps expected). \n", "\n", "Next, let's look at the *expected probability* for a specific value of the temperature. That is, we average over all samples from the posterior to get a likely value for $p(t_i)$." ] }, { "metadata": { "colab_type": "code", "id": "EIzyJL_3IA0P", "outputId": "960703b4-a5e8-4af4-a2b3-fbf53a03fe5d", "colab": { "base_uri": "https://localhost:8080/", "height": 53 } }, "cell_type": "code", "source": [ "alpha_samples_1d_ = posterior_alpha_[:, None] # best to make them 1d\n", "beta_samples_1d_ = posterior_beta_[:, None]\n", "\n", "beta_mean = tf.reduce_mean(beta_samples_1d_.T[0])\n", "alpha_mean = tf.reduce_mean(alpha_samples_1d_.T[0])\n", "[ beta_mean_, alpha_mean_ ] = evaluate([ beta_mean, alpha_mean ])\n", "\n", "\n", "print(\"beta mean:\", beta_mean_)\n", "print(\"alpha mean:\", alpha_mean_)\n", "def logistic(x, beta, alpha=0):\n", " \"\"\"\n", " Logistic function with alpha and beta.\n", " \n", " Args:\n", " x: independent variable\n", " beta: beta term \n", " alpha: alpha term\n", " Returns: \n", " Logistic function\n", " \"\"\"\n", " return 1.0 / (1.0 + tf.exp((beta * x) + alpha))\n", "\n", "t_ = np.linspace(temperature_.min() - 5, temperature_.max() + 5, 2500)[:, None]\n", "p_t = logistic(t_.T, beta_samples_1d_, alpha_samples_1d_)\n", "mean_prob_t = logistic(t_.T, beta_mean_, alpha_mean_)\n", "[ \n", " p_t_, mean_prob_t_\n", "] = evaluate([ \n", " p_t, mean_prob_t\n", "])" ], "execution_count": 54, "outputs": [ { "output_type": "stream", "text": [ "beta mean: 0.32857734\n", "alpha mean: -21.576159\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "code", "id": "Ri4BriJHPJNg", "outputId": "759de914-4b8f-4b45-b988-702159d3b246", "colab": { "base_uri": "https://localhost:8080/", "height": 299 } }, "cell_type": "code", "source": [ "plt.figure(figsize(12.5, 4))\n", "\n", "plt.plot(t_, mean_prob_t_.T, lw=3, label=\"average posterior \\nprobability \\\n", "of defect\")\n", "plt.plot(t_, p_t_.T[:, 0], ls=\"--\", label=\"realization from posterior\")\n", "plt.plot(t_, p_t_.T[:, -8], ls=\"--\", label=\"realization from posterior\")\n", "plt.scatter(temperature_, D_, color=\"k\", s=50, alpha=0.5)\n", "plt.title(\"Posterior expected value of probability of defect; \\\n", "plus realizations\")\n", "plt.legend(loc=\"lower left\")\n", "plt.ylim(-0.1, 1.1)\n", "plt.xlim(t_.min(), t_.max())\n", "plt.ylabel(\"probability\")\n", "plt.xlabel(\"temperature\");" ], "execution_count": 55, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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3AKP4/oe+GN+zw3H6TXxA/3gDH6HZ7c6HRq7/pM+FcRwU/HK4b83EB/FB1ScA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BBC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\nra/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gUl2GDx/OkiVL6Ny5Mx988IHbJ5Q6dOjgtU+TJk0YMWIETz/9NPPmzXO7of971AZE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\nBjwfWAzsCLwVuAF4Zdvmaeul99L6t6Sd7kZzgfxk4Hk0/3k8gOauo2XAaV1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" ] }, "metadata": { "tags": [], "image/png": { "width": 843, "height": 282 } } } ] }, { "metadata": { "colab_type": "text", "id": "iI7Fosv1IA0T" }, "cell_type": "markdown", "source": [ "Above we also plotted two possible realizations of what the actual underlying system might be. Both are equally likely as any other draw. The blue line is what occurs when we average all the 20000 possible dotted lines together.\n" ] }, { "metadata": { "id": "k_rZvVwz7zHI", "colab_type": "code", "outputId": "d8a00a3d-4fbc-4362-a670-999f76c94e14", "colab": { "base_uri": "https://localhost:8080/", "height": 302 } }, "cell_type": "code", "source": [ "from scipy.stats.mstats import mquantiles\n", "\n", "# vectorized bottom and top 2.5% quantiles for \"confidence interval\"\n", "qs = mquantiles(p_t_, [0.025, 0.975], axis=0)\n", "plt.fill_between(t_[:, 0], *qs, alpha=0.7,\n", " color=\"#7A68A6\")\n", "\n", "plt.plot(t_[:, 0], qs[0], label=\"95% CI\", color=\"#7A68A6\", alpha=0.7)\n", "\n", "plt.plot(t_[:, 0], mean_prob_t_[0,:], lw=1, ls=\"--\", color=\"k\",\n", " label=\"average posterior \\nprobability of defect\")\n", "\n", "plt.xlim(t_.min(), t_.max())\n", "plt.ylim(-0.02, 1.02)\n", "plt.legend(loc=\"lower left\")\n", "plt.scatter(temperature_, D_, color=\"k\", s=50, alpha=0.5)\n", "plt.xlabel(\"temp, $t$\")\n", "\n", "plt.ylabel(\"probability estimate\")\n", "plt.title(\"Posterior probability estimates given temp. $t$\");" ], "execution_count": 56, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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fl8sHUF1Vy9jYqJsvV667TVl5LJc3GPblyptqiNl4VYxQsASAzp4Wzpybuglh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\n3/b76PF49BgS4O8jlvbn48HlcuH3+xkzZsx+60PkQNp+ZdLu/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LmuE22u68Sho7s5cHgH\nNWuEOh8Eg0G+WDCDtq27UK9O00oeqRDictHpdBgMegwGPVabkWAwiN8fwOcN4PP6cTm9+PLd+H0B\n9GpBcdCkLw6dFAyaSkSUqThwMoUrnWw2IzpFbnAQQohrmS4YDFb2GMR58vLylgPdK7JtamoqAImJ\niVdwRFcnl8sFUG54JIQo32/xvpHvW6KqOXjwIBAK+oUQFSPvm18uP9fJ8m/3kXo0B68nNCeToujQ\n6xVMFgNWmxGjSZVqpirI4XAAXPKNaJdi38Ft/PPdsQA0bdSGfr2GcV3TZPl6Elet3+J9U5UEg8FQ\n4OTz4/P68RaHTwF/IBw0naty0mPQ9OHAqaTSKdJuxmLT5PvGVUx+TxPi0l2F75sVUVFRPS7HgaRy\nSQghhBBCCCGuApF2M4NGtGHfjlP8uOIIhXmu4rvP/RTm+Skq9KBpemyRJswWg7QxEpekRlwi/XoN\nY/maBew7uI19B7dRs0YSN3a/lZR2vdE0abEtRFWm0+kwaPoyc/oFAsHiwCn086bI5cbnDRAIBsk8\nmX+uwqk4eNKMoUonezUL8bUiqVErCtUgczkJIURVJOGSEEIIIYQQQlwldDodzVrXpMl1NTh68Aw7\nNqZyKjUXny+A3xfA6fTidvtQVQWT2YA1woTRJH/2iZ9nj6rOHYMfYsCNd7Fi7UKWrviCkxnH+ODT\nN1i8bC4T/zYDRZHAUohrjaLo0DQVTSu9PBAI4vOGqpx8vgCFxaFTMBgMh00mswGzVSOhdhQJiXbi\nEiIxW7Xyn0gIIcRVR/7KEEIIIYQQQoirjKJXaNA0jgZN4yjIc7JjYyoHd5+mIN+F3xfE6/Hj9fhx\nODxYrBqRUeYyd6MLUR6L2Ub/3ndyY/db2bRtJUtWzKNFk3bhYMnldpKRmUpSYuNKHqkQojIpig7N\nqKIZS19aDPgD+HwBPB4/BfluzuYUkZPl4NC+TIxGFXt1KzVqRRITH0G1OBtGo1yaFEKIq5V8BxdC\nCCGEEEKIq1hElJnOfRrTsUcD9m47yd7tpzhzuhCfz4/fF6Agz4XT4cEaYcQWacIg7YlEBaiqgZT2\nvenYrhd+vy+8fM2GxcyZ9w6N6rfkxu63cn3LG1AU+ZoSQoQoegVNr6AZVWwRRvy+AC6nF6fDS16O\nk5wzDtKPn0XT9BiMKpF2E9VjbVSLtWGvbiHKbkavSpWkEEJcDSRcEkIIIYQQQogqQFX1tGyfSMv2\nieTnOtm0+igHd5/G7fLh8/nJO+ukqNBT3C7PiNGkyqTr4mfpdDpU1RD+3OfzYjZZOHhkJweP7CSm\nWg16dhlEl479sFmjKnGkQojfI72qYI0wYo0wEgwG8bh9uN0+CvPdeL1FZGcWkn7sLJqmomp6DAaF\nCLuZqGgL9mqhj1HVzJjMBvmZJYQQvzMSLgkhhBBCCCFEFRNpN9NrYHPadkpizfcHST2Sjcftx+fz\nU5Dvp8hxLmQyW+SCnai4vj3voFunAazdsJj/rfySzDMnmfv1+3z57SyG9r+P/r3vrOwhCiF+p3Q6\nHUaTAaMpFFgHg0G8Xj9etx+3y0dhgRu/L0DW6UIMhlDQpBr0GDQ9ZotGVLSZqGqW0MdoC5F2E4pe\nqpyEEKKySLgkhBBCCCGEEFWUvbqFAcNacyYjnx9XHuHEkRx8ntDk645CNy6nB81oINJukrvCRYWZ\nTRZ6d7uFnl0Gs3PvRpat/ppd+zZSLTouvE1BYS6aZsKomSpxpEKI3zOdToemqWjaucuTwWAQn9eP\n1xvA5/Xjcrrxef2g02HQFAwGfShwMoTa6tmrmYmOsRJd3UJ0dSuRdjM6RX6WCSHEb0HCJSGEEEII\nIYSo4mJqRDJgWBschW62rT/B7q3puJ1e/P4AziIPHo8Pk8lARJRJ2uWJClMUPa1bpNC6RQqZZ05S\nzR4bXjdvwQw2b19F5w596dllEPGxtStxpEKIq4VOp8OgqRi0c8uCwSB+fyh0CgVOXgrzXfj9Ac5k\nFGDQ9OF/RpOBajFWoqqZiYo2E2kP/VNlvkEhhLjsJFwSQgghhBBCiGuE1Wakc59GtOtcl12b09mx\nKQ1HvqtUJZPJHGo9pBnlz0VRcXExNcOPg8EgWdmnKHIWsnTFPJaumEeLJu3o0XkQrVqkoOrla0sI\nUXGhud90qKoC5nNzwAUCQbweH15PKHAqyHMRCAbJOpUfrm5SNT2qQcEWaSLKbiYy+lzoZIswSls9\nIYT4FeQ3OiGEEEIIIYS4xpjMGu271KNVciIbVx1lz9Z0XMWVTKGQyYs1wkhEpBGDJn82ikuj0+kY\n9/C/OJZ6gGWrv+bHLT+we/9mdu/fTKTNzn0jxtK6RUplD1MIcZVTlNJzOAH4/QG8nuIKJ5cXX4Eb\nv8/PGbXgXOBkCAVOBk0lMspEZHHYFBVtJsJuxmrTpIJXCCEqQP5KEEIIIYQQQohrlGZUQ5VMNySx\nee1R9u3MoKjQjc8ToCDXSVGhG5PZgDXCKHMyiUuWlNiYP4wYyx2DH2LtxiWsWv8dJzOOE1s9IbzN\n6ax0oqNi0DRjJY5UCFFV6PUKenPpCqdgMIjPFwi31StyePB5/QT8AbLOD5uKHxtNKhFRpnBLvcji\niiezRX4OCiHE+SRcEkIIIYQQQohrnMlioHOfxrRJqcuPyw+zf1cGXrcfvz9AYYEbZ5EHzahitmiY\nzAYMml4usIkKs1kjuanH7dzY/TbSTh6hZo264XXTPnyZ01npdGrfh64p/alTu2EljlQIURXpdDoM\nxVVL5wsEiudxKg6eHC43Xm+AYDBYHDQpoeBJDX00mg2hSie7mUi7iYji4ElCJyHEtUrCJSGEEEII\nIYQQQGhOpl4Dm9M6OZFNa45x4kg2LqcXnzeA0+HF7fKhVxRUTZGgSVwynU5HYq0G4c+dLgc6nQ6n\ny8EPq+fzw+r5JCU2pnPHvnS4vgc2a1QljlYIUdUpig7NqPLTwsmAP4D3vEonV5EXn89PEDCo5YRO\nJpVIuzlc7VTy0SLt9YQQVZyES0IIIYQQQgghSqkeH0HfW1viKvKybcMJdm9Jp8jhJuAP4vf78Tr8\nuJ0+FH3owpzVZsRsMcjE6OKSmE1W/u/Jd0lNP8yq9d+xbtP/OJZ6gGOpB/jvl1N46s+v0aRh68oe\nphDiGqPoFYx6BaOx9GVTvz+AzxvA5ysndErPD4VO54VPmrGkvZ6JiKhQ6BQVbcZqM6JTJHQSQlz9\nJFwSQohK8Morr/Daa6/x9NNPM378+MoejhBCCCFEuUwWAyk9GpDctR4njmSzb/spTp44i9Phxe8P\nEPAHKXJ4cDm9qKqCNcKI1WZE/UnrISEuJrFWA+66bQy3D3qQrTvXsHbjEo4c30dSnSbhbX7c/ANx\nsTVJSmwilQBCiEqh1yvo9QpGLhY6BXC5vPi8foJBwtVNJYGTwaDHoOmJtJuJijYTHWOleqyNyGgz\nigROQoirjIRLQohr1oABA1izZg3ffPMNXbt2rezhCCGEEEL8bun1CvUaxVKvUSwBf4D0E7ns3XaS\n44fP4Cry4vcH8Xj8eHOKKMhzYbYYMFuNmMwGuVgmKkzTjHRs14uO7XrhdBVh1EwAeDxuZs99E6er\niIT4OtyQfCMp7ftQzR5bySMWQogLh04BfyA0n1Nx6FTkcuPzBggEg2SezMeghYImTVPRTKEqJ1uk\niYhIU7jKKSLKJFXBQojfLQmXhBCiEjz00EPcdtttVK9evbKHIoQQQghxSRS9QmK9aiTWq4bX42fP\ntnT27TjFmdOF+H0B/D4/Bfluihxe9KoOo9GA0aRitmro5QKZqCCzyRJ+7PG66dKxH+s3/8Cp0yeY\nt2AGXyz8D00btaFj2160b9MNs8laiaMVQoiyFL2CplfQftJeLxAI4vP68Xr9eFx+CvPdBAJBVFVB\nf16lU6jKSSUyykSE3UykPTSXU6TdhDXCJDdvCCEqnYRLQghRCapXry7BkhBCCCGuegZNT+sOdWiV\nnEhGeh5b1h4n9WgOHrePgD+Axx3A4/bjKNShP+vEYtWwRhjLXGgT4mJs1kiG3/IXbh/8ELv3bWLN\nhiVs37WOvQe2svfAVurXbUathFC4FAwGpW2eEOJ3TVFC8xVqRhVsoWUlgZPfF6p2cjm8FHhdBAIB\nsk6da6tXMqeTQVOJrm4htkYEsTUiqB5nk5a0QojfnNw2Jqq0TZs28dxzz9GjRw8aNWpEbGwsTZs2\n5d5772Xjxo1ltr///vux2+1MmTLlgsecNm0adrude++9t9znu//++2nevDmxsbE0aNCA4cOHs27d\nunKPZbfbsdvtAHz44Yf07t2bxMRE7HY7ubm5AOzbt4+XX36Zm266iaZNm4aPe8cdd/C///3vguMM\nBoPMmjWLrl27UqNGDRo0aMDIkSPZvXs3H3/8MXa7nT//+c/l7rt//37GjBlDq1atiI+Pp27dugwZ\nMoRvv/32gs93IS1btsRut3P8+HHmz5/PTTfdRO3atalTpw633HLLBV8bgOzsbF544QWSk5OpUaMG\niYmJ9OnTh+nTp+Pz+crdZ968eQwaNIikpCRiYmKoX78+N9xwA2PHjuXo0aMArFq1Crvdzpo1awAY\nNGhQ+P/CbrezatWqUsdMS0vj6aefpn379uFx9O3bl48//phgMFhmDAMGDAgfZ82aNQwbNoz69esT\nHR3NggULgNCcS3a7nVdeeaXc81i8eDG333479evXJzY2lhYtWjB69Gj279//s6/zggULGDhwIHXr\n1sVut7Njx44LvsZCCCGEEJeDTqcjobadAcNac++YG+jUswFxCZGYLAY0TY+i6PD5/OTnOsk8lc+Z\n0wU4izzl/i4lxIWoepXWLVL4yx+e542Jn3HvnU/QNaU/tRKSwtv8852nmPrBS2cOF0cAACAASURB\nVGzduQavz1N5gxVCiEtQEjiZrRoRUSaiY6zEJUQSlxBFZLQZzWgIzXNY6CYny8Gp1FwO7jnNpjXH\n+GHBXr6es5Xl3+5j95Z0Tp/Mx+fzV/YpCSGuAXK7mKjSJk6cyOrVq2natClt27bFaDRy6NAhvv76\naxYuXMiMGTMYOnRoePu77rqLL774gjlz5lwwePnkk0/C255v8uTJPP/88wC0bt2a5ORkTp48yZIl\nS1iyZAmTJk1i1KhR5R5z3LhxzJgxg44dO9K3b18OHToUvtvu3XffZfbs2TRp0oTrrruOiIgIjh07\nxtKlS1m6dCkvvfQSY8aMKXPMxx9/nA8++ABVVencuTMxMTFs3bqVPn36MHLkyAu+ZvPmzePPf/4z\nHo+HZs2a0bdvX86cOcO6detYsWIF48aN49lnn73Iq16+qVOnMmXKFNq3b0+/fv3Yv38/y5YtY+XK\nlWX+HwCOHDnC4MGDSUtLIz4+nn79+uF0Olm1ahVjx45lwYIFfPrppxiNxvA+r7zyCq+99hoGg4EO\nHTqQkJBAXl4eJ06cYPr06XTq1Il69eoRHx/PiBEj+P7778nMzKR3797ExcWFjxMfHx9+vHLlSkaO\nHEl+fj7169end+/eOBwONm3axMMPP8zKlSt57733yj3n+fPn85///IemTZvSs2dPsrOzMRgMP/ta\nvfjii0yaNAlFUUhJSaFmzZrs3r2b//73v3z11Vd88MEH9O3bt9x933nnHd5//33atWvHjTfeSHp6\nOooi9xEIIYQQ4rdjsRpJ7lqf5K71KXK4ObIvi/27Mjidnl98V7afwgI3ziIvmlGPLcKE2apJex9x\nSayWCLp3GkD3TgPCy3Jys9h/OHRj1catyzGbrLRt1YUObXvSrNH16PVyV78Q4uqiKLrQnExa6eWB\nQBCvx4fb5SM/14nP5yc7s5Djh86gmVSMRpVqsTZia0QQE2+TyiYhxBWhkzvFfl/y8vKWA90rsm1q\naioAiYmJV3BEVyeXywXA6tWradWqVangAOC7777j3nvvxWazsXv3biyWUD9vv99Py5YtOXnyJKtX\nr+a6664rtd++fftISUkhPj6e3bt3o6qhfHbp0qXccccdJCQkMHv2bNq3bx/eZ/369QwbNgyn08m6\ndeto2LBheF1J1VJkZCRffvkl7dq1K3Muq1evJjExkbp165ZavmnTJm699VacTifbtm2jVq1a4XUL\nFixg5MiRREVFMX/+fNq0aQNAIBDghRdeYPLkyQCMGDGiVJXWrl276NWrF5qmMXPmTG688cbwur17\n93LHHXeQlpbG119/Tbdu3S76f1CiZcuWpKamoigKM2bM4JZbbgmvmzFjBk899RQRERFs2rSpVKjT\nq1cvtmzZwtChQ5k6dSomU2gy37S0NIYOHcqhQ4d44okneOGFFwBwu90kJSWh1+tZvnx5qdcZ4PDh\nw+j1epKSksLLBgwYwJo1a/jmm2/o2rVrmbFnZGSQkpJCQUEBkydPZsSIEeHQLy0tjREjRrBz507e\nffdd7r777jLHBXjzzTe57777yhy7JAh7+umnGT9+fHj5kiVLGDZsGFarlc8++4zOnTuH17399ts8\n//zzREZGsnnzZmJjz01gXPI6q6rKxx9/fMHw6WJK3jclr/WVIN+3RFVz8OBBABo1alTJIxHi6iHv\nm2tXTlYhG1cf49iBLNxuH35fgEAgiKLoMBj0mK0aFquGQdNLW7OfcDgcAFitMq/QzzmTncGGrcvZ\nsHUZqemHw8tt1iieGP0KSYmNK3F04rck7xtxLQkEgnjcvvA/ny+ApunD7fc0k0q1GCsx8TZi4kNt\n9MprUSu/pwlx6a7C982KqKioHpfjQHI7u6jS+vTpUyZYAujfvz9Dhw7l7NmzpVqg6fV67rzzTgDm\nzJlTZr+SZXfccUc4WAJ49dVXgdDF//ODJYCUlBTGjRuH1+tl5syZ5Y7zscceKzdYAujSpUuZYAmg\nffv2PPjgg3i93jLt6koqacaMGRMOlgAUReH5558vFUSd7/XXX8fj8fDiiy+WCpYAmjVrxssvvwzA\n+++/X+7+FzNw4MBSwRLAAw88wA033EBBQQGzZ88OL1+7di1btmwhIiKCSZMmlQo7ateuHX69p0+f\nHg5ECgoKcDqdJCUllQmWABo0aFAqWKqIKVOmkJuby5gxY7jrrrtKXeSoXbs2b7/9NhBqlVienj17\nlhssXcw777wDwOjRo0sFSwCPPvooycnJ5Ofn88EHH5S7/9133/2LgiUhhBBCiCutWqyNvrdcxz1j\nbqB95yTs1SwYjSo6nQ6320fe2SIyT+WTlVGAo8BNIBCo7CGLq1BM9Rrc3Gc4fx/3HhP/NoPBfe8h\nPrY2bo+ThLhzNzitWLuALTvW4PG4K3G0QghxeSiKDpPZQKTdTEx8BHEJkVhsRgKBIPm5TjLS8ji4\n5zSb1x5n2cJQG70lX+1i3Q+H2LExlcP7MslIy8Pp8BEISCGCEKJipC2eqPKys7NZtGgRe/fuJS8v\nLzxXz549ewA4dOhQqYvxd911F5MmTWLu3LlMmDAhHCL5/X4+++yz8DbnH3/z5s1ERkbSq1evcsdQ\nEhKUN88ThOb8uZiCggKWLFnCzp07OXv2LB5PqHf4kSNHwudQwufzsWHDBiAUgv2UwWBg8ODBZeaV\nCgQCfP/99+h0OoYMGfKLzuNihg0bVu7y4cOHs3btWlavXs3YsWMBwlU//fr1Izo6usw+ffr0oUaN\nGmRkZLBt2zZSUlKIiYmhTp067Nq1i2effZZRo0bRuPGvuytx6dKlAGVa9pVo06YNNpuNnTt34nK5\nylT8/Nz/60/5fD5+/PFHoGzbxRJ33303GzduLPV6/ZrnFEIIIYT4rVmsRm7o3YiO3Ruwb9cptq07\nQW5OEX5fAL8vQJHDg9vlRc3VY7IYMJoMmMwGaZsnLlnNGnUZ0n8Ug/vdy9ncLIxGMwA+n5e5X7+P\n0+VA00y0bNaBdq270qp5R8wmSyWPWgghfr2SsMlkDrXmL2mj53H7KMx34/UWkZ1ZiF5V0KsKqqqg\n1yu4PS70eh2HdzixRhix2oxYI4xYbEZsEUYsNg2T2SAVxkIIQMIlUcXNnDmTZ599lqKiogtuU1BQ\nUOrzRo0a0aFDBzZs2MDSpUvp378/AMuWLSMjI4M2bdrQvHnz8PbHjx8HID8/n+rVq190PGfOnCl3\n+cVahC1cuJAxY8Zw9uzZCp1DdnY2brcbRVEuWKFU3vPl5OSQn58PUG7lz/kudB4XU171FUCdOnUA\nOHnyZHjZqVOnLroPQFJSEhkZGeFtITSv06hRo3j33Xd59913iYmJoX379vTu3Zthw4YRFRV1SWM+\nduwYEKpA+jk5OTnUrFmz1LJLbf2Wk5MT/r+70L4l1Vfnn/eveU4hhBBCiMqiVxVatKlF89Y1ycrI\nZ/uPqRw7dAZXkRe/P4jb7cPj8aEobvSqgtWmYbEaMWgyZ4S4NDqdjmrR5zpa+Pw+bu4znM3bV3Es\n9QCbt69k8/aVqKqBFk3aM7T/KOrUvvjfREIIcTVRFB1GU+iGDYBgMIjX6w/f2OF1+3H6vbhdXgKB\nII787FKhU0kIpVcVDAY9FpsWDp6stlDoZCn+XJP2tkJcMyRcElXW1q1befLJJ1FVlYkTJ9KvXz9q\n1qyJxWJBp9MxYcIE3njjDcqbd+yuu+5iw4YNzJkzJxwuffLJJ+F15/P7/UBo3qQBAwZwMRcKn8xm\nc7nL09PT+eMf/4jT6eTJJ5/ktttuo06dOlitVhRFYdasWTz++OPlngNwwR/milK2I2bJeej1+gtW\nGf3e3XDDDWzfvp3FixezevVqfvzxRxYvXsyiRYt49dVX+eKLL2jdunWFj1fymtx6660YjcaLblve\n+l8zd9Ev/UXsSs6XJIQQQghxJeh0OuISorhxaBRej58929LZs+0kOVmO4nmZAnjcPrweHwV5Lkxm\nA1abEZNF7pwWv4zJaObmPiO4uc8Iss+eZsv21WzesYpDR3ezffc6bh14f3jbg0d2YTZZqJVQT77e\nhBBVhk6nQ9NU0EovdzgcBINBTCZzOHjy+QN4nd7Q5/4AwSDo9Tr0qj4UQJ33WK/XoRnV0oFT8eOS\njzK3ohBVh4RLospauHAhwWCQP/3pTzzyyCNl1pe0lCvPLbfcwvjx41m8eDE5OTno9XoWLlyIpmll\nWs2VVAcZDIYyreZ+rcWLF+N0Ohk8eDDPP/98hc6hWrVqaJqGx+MhLS2t3HmGTpw4UWZZ9erVMZvN\nOJ1O/vnPf2Kz2S7LOZz/nC1btrzgWBISEsLLSh6XVIWVp6Sq6Pz9ACwWC7fcckt4fqeMjAyeeeYZ\nvvjiC8aNG8eSJUsqPOZatWpx5MgRxo0bR7NmzSq83y9VrVo1jEYjbrebEydO0KBBgzLbXOi8hRBC\nCCGqAoOmp3WHOrTuUIfszEIO7Mrg6MEszp4pwucL3WFdWODGWeRFNSiYLRpmiwGteO4mIS5V9eh4\nbuxxGzf2uI28/Bx27dtErRpJ4fWffjWFoyf2Uz06ntbXpdC6RSeaNGyFQdUufFAhhLiK6XQ6VFWP\nqpZfKRwIBMNBU8lHj9uDr/gxULbiSX/uo2ZSsVq1cPhksWpYI4yYrRpWmyY/04W4iki4JKqs3Nxc\ngHJbw505c4Zly5ZdcN+oqCgGDhzI3Llz+fzzz9E0DZfLxeDBg8vMAVSzZk2aN2/Onj17WLVqFV27\ndr1s51DSCq+8c3C73Xz99ddllhsMBpKTk1mzZg3z5s3jqaeeKrXe6/WWu5+qqnTv3p1FixYxf/58\n7r777st0FiFz584tt7KrZB6rLl26hJeVzO20aNEicnNzsdvtpfb5/vvvycjIwGaz0aZNm4s+b40a\nNXjuuef44osv2LVrV6l1mhb6g7CkQumn+vTpw7Rp0/jqq69+k3BJVVU6duzIypUr+eSTT/i///u/\nMtvMmTMHKP16CSGEEEJURdXjbHTq1ZCUng04nZ7HlvUnOHE4G4/bh98XwO0qmTtCQTXosVg1TBYD\nBoPcES1+majIanTucFP480DAT+2a9cnOOU322dP8sGo+P6yaj8looUXT9vTpdguNG5S9gU4IIaoy\nRdGhaHoMlA2fgsEgwUAQvz9QHDYF8XlDP7P9FwqfSoVQOgyaGgqeSgIoq/G8xxomiybzMArxO1G2\nN5YQVUTJvEH//e9/KSwsDC8vKCjg4YcfJi8v76L7l7S/mzNnzgVb4pV49tlnAfjTn/7EDz/8UGa9\n3+9nxYoVbNy48ZLOoVGjRgB88803ZGZmhpd7PB7++te/hqtYfuqhhx4CYPLkyezYsSO8PBAI8NJL\nL5GWllbufk8//TQGg4Hx48czb968Mu32gsEgmzdvLvccf87XX3/N/PnzSy2bNWsWq1evxmazcc89\n94SX33DDDbRt25aCggLGjh2L2+0Orzt58iTjx48H4MEHHwy3gTtx4gQffvhheN6o83333XdA2fmI\nSqp/9u/fX+6YH330USIjI3njjTd4//338fl8ZbbZu3dvuWHdL/Xwww8Dofmj1q9fX2rdO++8w4YN\nG4iMjOTee++9bM8phBBCCPF7ptPpqFHbzs23t2LUI53p2K0+1eNsmEwqqqonEAjicno5m+0g82Q+\nmacKKMh34fOWfwOREBWlKHruG/4Ur0/4jGcfn8yAG++idkI9XO4iNm9fSW7eublo004e4dDR3Re8\ncU0IIa4FOp0ORa9g0FTMFg1bhJGoaDPVYqzE1oggvmYkcTUiiIo2Y7ZoKHoFvz9AkcNDbnYRWacK\nSD9+liP7s9i7/RTb1p/gxxWHWbl4P0vn72bBp9v5avZmvvt8BysW7WPjqiPs3pLOsYNZZGXkU+Tw\nXHDqCCHE5SeVS6LKGj58ONOnT2f79u20adOGlJQUgsEga9euRdM0Ro4cyUcffXTB/bt3707t2rXZ\ntm0bAPHx8fTp06fcbQcMGMBLL73ECy+8wK233krDhg1p2LAhNpuN06dPs2PHDvLy8njjjTdITk6u\n8DncfPPNtGrVih07dtCuXTs6d+6MyWTixx9/JD8/nz/96U+89957ZfYbMmRI+Px69epFly5diImJ\nYevWraSnp/PAAw8wY8aMcOVOieuvv56pU6cyZswYHnjgAf7+97/TtGlToqOjOXPmDDt37iQrK4vH\nH3+cXr16Vfg8IBS8jRo1iuTkZOrWrcuBAwfYsWMHer2et956ixo1apTafvr06QwaNIjPP/+c1atX\n06lTJ4qKili9ejUOh4Pu3bvzt7/9Lbx9bm4ujz76KGPHjqVly5bUrVuXQCDA/v372bt3LwaDgRdf\nfLHUcwwcOJA5c+bw/PPPs2zZMmJjY4FQqNSoUSNq167NRx99xKhRoxg3bhyvv/46TZs2JTY2lry8\nPPbs2UNaWhq33norgwcPvqTX40L69u3L448/zptvvsnNN99Mp06dSEhIYM+ePezZsweTycS0adOI\ni4v7+YMJIYQQQlQxZotGxx4N6NC9PpmnCti9JZ0Th8/gKHDj94fulHY6PLhdXvL1CkZT6OKWyWJA\nr5d7K8UvoygK9ZOaUT+pGbcOuJ8z2Rls37Oe65qe+9tuyfJ5rNmwGIvZRvMmbbmuaTLXNU0m2h5T\niSMXQojfF51Oh05fEkCVv02ptnvFrfe8Hm/4cTAQRPlJ1ZN6XvWTpumxRBixRZiwRhixRRpDHyNC\nFVCK/D4gxGUj4ZKosux2O8uWLePll19m2bJlLFmyhNjYWAYNGsQzzzzDzJkzL7q/oigMHz6cf/3r\nXwDccccdqOqF3zJjxoyhe/fuTJs2jdWrV7N8+XJUVSU+Pp4bbriB/v37M2jQoEs6B1VVWbhwIf/6\n179YuHAhy5Ytw26306VLF/72t7+xYcOGC+779ttv07ZtW/7zn/+wbt06LBYLKSkpzJo1i0WLFgGh\neZZ+6rbbbqNt27ZMnTqV5cuXs2bNGgDi4uJo2bIlN910E0OGDLmk8wAYPXo0ycnJ/Pvf/+a7775D\nURR69OjBuHHjwm3wzle/fn1WrlzJW2+9xbfffsu3336LwWCgadOmDB8+nPvuuw+DwRDevl69evzj\nH/9g9erV7Nu3j3379qEoCgkJCdx3332MHj2apk2blnqOm2++mddff52ZM2eyYsUKnE4nAMOGDQtX\njXXr1o3169czbdo0Fi9ezKZNm/B6vcTFxVG3bl0eeOABhg4desmvx8X8/e9/JyUlhffff58tW7aw\nYcMGYmNjufPOO3niiSfKnIcQQgghxLVGp9MRXzOS+JqRBAJBTqXmsntLOqlHc3A6PMXtePx4C/w4\nizzo9QpGc6hlnqapGE0qOmmpI36hmOo16N219N8AsdUTiI+txemsdDZtW8mmbSsBqJ1Qj+6dB9Kr\ny6X/DSWEENeii7Xdg1BXnXPzPYWCKLfbh88RwO/zEwwSCpyKwyfVUPxR1aNXFSw2DVukCVtkKICy\nRRqxRZqw2iR4EuJS6aRU8PclLy9vOdC9ItumpqYCZVt9CXC5XADhlmmitCFDhrBixQo++OCDXxQU\nXYqWLVuSmprK9u3bqVu37hV9LvHr/BbvG/m+JaqagwcPAufamAohfp68b8SV5PP5OXrgDHu2ppOR\nlhean6m4okkH6BQdiqJDr1cwWzXMFg3N+Pufo8nhcABgtVoreSTi52SeOcmufRvZtXcT+w5uxe1x\nMajvPQztPwqA01lpbNmxhmaN2lCndkMUpfyLp+LXk/eNEJeuKrxvSiqffD5/KIDyBfAVh1EBfwCl\nJHhS9ajhx6H5G602Y6n5nqw2I2bLufmeJHwS5bkK/75ZERUV1eNyHEgql4Soovbu3UvdunWxWCzh\nZV6vlzfffJMVK1YQExPDTTfddJEjCCGEEEIIcXVRVT2NmsfTqHk8brePfTtOsX/HSbIyCvH7Q610\nAoEgPp8Pj8dHYb4LTVMx2zQsFg29KheNxK8TF1OTXl2G0KvLELw+D4eO7CamWnx4/bZd6/j8m/cB\nsFgiaNqwNc0aXU+zxtdTIy7xdx90CiHE71248kkrG94HgyXBU3Ho5PXjdnrxFQdP57faO/dRh15f\nXPVk1bBEhEIna3GbPWtE6LHJbJDv4eKaI+GSEFXUpEmTWLBgAa1btyYhISE8R9CpU6cwGo38+9//\nxmw2V/YwhRBCCCGEuCKMRpXWyYm0Tk7EUeDi2KFsTqfnc/LEWfJznfi8oQtLRUUeXC4v+aoTo1HF\naDZgMhlQDYpcJBK/ikHVaNb4+lLLkhIb0zWlP3sPbOVMTgZbdqxmy47VANRKSOLFv74vX3dCCHGF\n6HQ6VIMe1XDh4Olcy70Abqfv3NxP/sC5OZ7OD5+KPzcYQnM9lQRP58/zZLZpaJpchhdVj3xVC1FF\n3XbbbRQWFrJjxw62b9+Oz+cjPj6e4cOH88gjj9CiRYvKHqIQQgghhBC/CWuEiRbX16LF9bUIBoPk\nZDrYtvEER/dl4XR68PuC+Dx+vB4/RQ4PiqLDYNBjshgwmgwYjTJHk7g8mjRsTZOGrQHIOnOSvQe3\nsffAVvYd3Ep8bO1wsORyO5nwr9E0SGpB4wYtadygFXExNSV4EkKIK+RiwRP8ZK6n4vDJ5fSGH5fM\n9RSa3+m84Kk4hNKManF7PSPWiFBrXrNFw2w1YLJomM0GqaAWVx0Jl4Soovr27Uvfvn0rexjs3Lmz\nsocghBBCCCFEmE6no3q8jd4Dm+PvF+DA7gz2bE0nM6MAn9dPwB9qnecs8uJ2eVH0oQtFJrMhVNVk\nVlEUufgjfr3YmJrExtSkW6ebCQaDOJ2O8LrDx/ZwOiud01nprN24BICoyGo0rh8Kmjq07YnNGllZ\nQxdCiGuOTqdDVfWoavnhU8lcT6E5nvzhlnuhqqcgOh2lW+7pFRRVd+6xosNoUjFbNEwWw3kfDZjM\nWuijJVRdLTe8iN8LCZeqOLvdfsF1b775Jvfddx8As2bN4vHHH7/gtrm5ueHH3bt3Z/v27eVuN2rU\nKN566y0Atm3bRo8ePS54zOXLl9OmTRsAHnvsMT744INSzyOEEEIIIYQQV5JeVWjWuibNWtfE7fJy\n7OAZjuzP4mRqLk6Hh4A/dJeyz+fD4/ahFLjQqwomsxYKm0wqepncW1wGOp0Oi8UW/rxZozY8P3YK\nBw7v5MDhHRw8sou8/Bw2blvBxm0ruL5l5/C2u/ZuxGK2Uad2Q1TVUBnDF0KIa17puZ5Kfy8OBkM3\nrpxruRd67PGEqp5Kft9QFF34pha9vuTxuWWKXoeqVzCaywmdzKGPZrNWXHmtSrWruOIkXBJCCCGE\nEEIIcc0zmgw0aZlAk5YJBAJBMtLz2L/jFKlHcyjIcxVf/Angcfvxepw4Ctzo9To0oxpqnWdSMWh6\nuZAjLgtF0VO3diPq1m7Ejd1vJRgMkpGZyoHDOziZcYJoe0x42zlfvMvprDQMBo26tRvRIKl5+J89\nqnolnoUQQggI3UCg14eqlNDK36YkgAoUVzqVfPS4/QT83tCyQIBgIIhSHDTpleKPeuUnQZQuXHV9\nfvBkMhvCN8iEPzepKHKjjPiFdMFgsLLHIM6Tl5e3HOhekW1TU1MBSExMvIIjujq5XC4ATCZTJY+k\ntI8//piHH36YESNGMGXKlCv+fC1btiQ1NZXt27dTt27dCu83YMAA1qxZwzfffEPXrl3Dy1955RVe\ne+01nn76acaPHx9evmrVKgYNGkTnzp1ZuHDhZT2H39LChQt5++232bNnDwUFBQCsXLmSVq1a/eJj\nXonXZs+ePUycOJENGzZw9uxZAoEA//jHP/jLX/7yq477W7xv5PuWqGoOHjwIQKNGjSp5JEJcPeR9\nI65G+blO9u88xeG9mWRnOfD7AgQCoYs+UHy3sqJDVRW04jmaNJOKqiqXJWxyOELt0qxW668+lqha\n/H4/s+e+ycEju8jITC2z/raBf+TmPsMBcHtc6PUqqv7auM9Y3jdCXDp53/z+heZ+CoVPAX8QfyBQ\nJpAqFUIpunDVU8lHRa+gV84FUZqpJHgKtf8NB1BmA0azGn4sN9GU7yr8+2ZFVFRUj8txoGvjNwoh\nRKUpac34e295uH37dkaNGgVAt27diI+PByA6Oroyh1WGw+HgzjvvJDU1lbZt29K7d2/0ej1Nmzb9\nzcZQVcJEIYQQQoiKirSbSe5an+Su9cnPdbJnWzrHD2WTnVlYHDQFCfiDuLw+3G4fDkWHoiioBiVc\n1WQ0GVBkjgRxmen1eu4b/hQAhY58jhzfy+Fjezh8bA9Hju+jds164W1XrvuWeQumk5TYmAZJzUmq\n04R6iU2oXi1eLhYKIcRVIjT3kw7Ui1cblQqhilvyhSqwAwQCvlJBlHJe0KQo5yqgzg+mQjfR6M+b\ngzIURJU8NprUc+tMBlTD5bnBRvy+SbgkhChj6tSpOJ1OateuXaHt27Vrx4YNGzCbzVd4ZFfOwoUL\n8fl8PPXUUzz33HOVPZwL2rx5M6mpqXTs2JHFixdX9nCEEEIIIa45kXYzKT0aktKjIW6Xl6P7szh6\n8AwZaXk4Ct0E/KG2Nj6fH6/Hj8vpLTVRdyhskosu4vKzWSNp1bwjrZp3BCAQ8HN+s5oz2Rl4vR4O\nHtnFwSO7Su13XdNkHrxn/E8PKYQQ4ip1KSFUyU0yJVXZgeK5oTzF1VHhau1g2ZZ85YVQer2Cqobm\nhjKaikMo03khlOXcjTdGswFNKqKuWhIuCSHKuNSWZRaLhcaNG1+h0fw20tPTAahfv34lj+TirpZx\nCiGEEEJcC4wmA01b16Rp65oEg0HOZjs4tCeTkydyOXO6AFeRN3y3sM8XwOPxU+TwlKlq0oxqaB4G\nIS4jRdGX+nzErX9hUN+7OXxsL0eO7+V46kGOnthPoSMPh7MgvJ3b7eTZV+6nTq2G1KvThKTExiTV\naUyEzf5bn4IQQogr7Nx8UAD6i24bDJS04QueVw0VxOf143H5zq3zB0FXGq/GiAAAIABJREFU3Da4\nnGqoUuGUokOv6ovDJrVUGHXuppzidcXhlKpefJzityPhkqjSzm/JNmvWLGbMmMGhQ4cwmUx07tyZ\nZ555hubNm190vw8//JAPPviAAwcOUFBQwLFjx8Lrs7Ozefvtt/n2229JTU3FYDDQpEkThg8fzn33\n3YeqXvgtlp2dzcsvv8yiRYvIzs4mISGB22+/nSeffBKLxVJqW6/Xy7x581i6dCnbt28nIyMDv99P\nnTp16NevH48//vjPtm+bP38+7777Lnv27EFRFNq1a8df//pXOnXqVGbbC825dCHltUkrmZ/pp69p\nidzcXMaMGcNHH33ECy+8wBNPPFHusd977z2efvpphg4dyqxZs352LBC66+LTTz9l9uzZ7Nq1C5fL\nRUJCAn369OHxxx8vVZH103E+/PDDPPzwwwCXNDfWggULmDx5Mrt27UJVVa6//nrGjh37s/ulpaUx\nefJkvv/+e9LS0jAYDDRv3px7772Xu+66K3znRslrXOKTTz7hk08+AUJh4M6dO8PrHA4H06dP56uv\nvuLQoUN4vV6SkpIYMmQIjzzyCDabrdyxbNmyhenTp7NhwwYyMzOx2WzUqVOHm266idGjR1OtWrXw\n1wbAmjVrSv2/Sps8IYQQQlzLdDod1WJsdOgW+l0rGAhy+lQ+B3ZlkHY0h9ycInzFLfRKqprcTi+6\n4gstmqbHaDKgGUNhk7TQE1eCzRpF6xYptG6RAoT+dso+m4nH4wpvcyL9MGdzszibm8X23evCy6vZ\nY0ms1ZBhgx+iRrzMoSqEENcanaJDVfQVShQCgVDFU6kgKhAKogLuc5VSAX+QYDCILhxAhcKo80Mo\n3XkVUYqiw6Dp0Yw/CZ5KHptDc18azwuo5AaeK0fCJXFNGD9+PO+99x6dOnXi5ptvZvv27SxYsIAf\nfviBefPmlRuwAIwbN44ZM2bQsWNH+vbty6FDh8IX+48cOcLgwYNJS0sjPj6efv364XQ6WbVqFWPH\njmXBggV8+umnGI3GMsfNzc2ld+/e5OXl0aVLF3w+H6tXr+Zf//oXK1asYP78+aUCpszMTEaPHo3d\nbqdx48a0bNmSgoICtm7dyltvvcX8+fP5/vvvqV69ernnMXXqVKZMmUL79u3p168f+/fvZ9myZaxc\nuZIZM2YwdOjQy/Aql9ayZUtGjBgRDkBGjBhRZpuHHnqIjz76iJkzZ/LYY4+hKGW/2c+YMQOAP/7x\njxV63mAwyEMPPcTcuXMxGAx06dKF6OhoNm/ezPTp05k3bx7z5s2jbdu2pca5fv16jh49SkpKCvXq\nhfqSX+jr4qfeeustXnjhBQA6duxIYmIie/bsYfDgwTz00EMX3G/lypWMHDmS/Px86tevT+/evXE4\nHGzatImHH36YlStX8t577wEQHx/PiBEjOHr0KOvXr6devXqkpIT+IDz//z09PZ3bbruNffv2ERMT\nQ3JyMkajka1bt/Laa6+xYMECFi5cWCbse+ONN5g4cSLBYJBmzZrRoUMHCgsLOXToEP/v//0/unbt\nSteuXenTpw8mk4nvv/+euLg4evfuHT7G1V69JoQQQghxOekUHTVqRVGjVhQAriIPB/dkcvRgFpnp\n+Tid3tAdwMVVTV6PH2eRN3Qx5bwLJwZNxe8PSNgkrgidTkdMtfhSyxokNecfz87i2IkDHD2xn2Op\nBziRdpCc3CxycrO4+/Yx4W0//nwyqScPk1irAXVqNSSxVgNq1UjCYNB+61MRQgjxOxL6faZiQVQw\neF7YFDhvrih/EJ/XF543qqR9X7lVUcW/P52rjlLCyzSTislkKBU4lRtMmVQ0TUUnv3NVmIRL4prw\nwQcf8M0339C5c2cg9E1rwoQJTJo0iQcffJBNmzZhMpnK7Pfpp5+ydOlS2rVrV2bdH//4R9LS0hg6\ndChTp04N71+ybPny5bz66qvh0OF83333HSkpKSxfvjx8kT8zM5OhQ4eyceNGXn31VSZMmBDePjIy\nkk8++YQ+ffpgMBjCy51OJ2PHjuXjjz/m5Zdf5o033ij3/N977z1mzpzJLbfcEl42Y8YMnnrqKR55\n5BE6depEfHx8ufv+UgMHDmTgwIHhcKm8CqBWrVrRqVMn1q1bx5IlS+jXr1+p9StWrODAgQM0a9aM\nLl26VOh5Z8yYwdy5c4mLi2P+/Pk0a9YMAL/fz/jx45k2bRqjRo1i06ZNGI3G8Dj//Oc/c/ToUe65\n5x7uvvvuCp/n9u3bmTBhAqqqMnv2bPr37x9e9/bbb/P888+Xu19GRgb33nsvDoeDf//734wYMSIc\nXKalpTFixAg+/fRTunXrxt13303jxo2ZMmUKH3/8MevXryclJaXMaxoMBvnDH/7Avn37ePDBB5kw\nYUJ4Hiyn08ljjz3GZ599xvjx40vt+8033zBhwgSsVitTpkxh8ODBpY67ZcuW8NfHE088Qfv27fn+\n++9p1KhRhSu7hBBCCCGudSaLRsv2tWnZvjaBQJDT6bkc2ptJ+vFczp5xhO7kDZTM1xRqoVcSNgWC\nAfR6HV63DoOmoml6DDI/gbhCFEUhPrY28bG16diuFxCavykz6ySpJw9TzR4X3vbAkZ2knTxSag4n\nRVFIiK/DDck30a/XsOL9A+h0OvmaFUIIUYZOp0Ov6tDz8xVGwWCQYJBSVVElj/3+IF6P79zcUcVh\nVXnBk14pWyVVss5oVNF+EjyFKqXU4nmjzrXuM2jXdos+CZfENeH+++8PB0sQ+qb1f//3f3z55Zcc\nO3aMr7/+mmHDhpXZ77HHHis3WFq7di1btmwhIiKCSZMmlQqmateuzauvvsrtt9/O9OnTefrpp8sE\nVzqdjtdff71U9UhcXByvvvoqgwcPZubMmTzzzDPh/SIiIkqFFiXMZjP//Oc/+fTTT/n6668vGC4N\nHDiwVLAE8MADDzBv3jzWrl3L7NmzK9TC7Up46KGHWLduHTNmzCgTLk2fPh0IjbWi3nnnHQCeffbZ\ncLAEoNfreemll8ItDOfPn1/u//mlev/99/H7/YwYMaLM/9Gjjz7KF198wbZt28rsN2XKFHJzc3ns\nsce46667Sq2rXbs2b7/9Nj179mTatGkVDrv+97//sWHDBpKTk3nttddKVYKZzWYmTZrEsmXLmDt3\nLq+88kr466+kLeDzzz/PTTfdVOa4JVVeQgghhBDi8lAUHQmJ0SQkhlpbez0+ThzJ4eiBLDLS8yjI\ndeHz+c9rJRPE7w3g8zjRKedawxiMoeomrThwUqTti7hCFEVPjfjEMu3wnvzza6SmHy7+d4gT6YfJ\nyEwj/dQxHI788HZHju9l0tTx1KxRl1oJSdRKqEetGnWplVCPyIhoCZ2EEEJUSOhGBS6pKio0V1Tp\nVnyBQBCvx0/A///Zu/P4uMp68eOf58ySbbKnadOkewulQBdoESi2ZXFBkE0QLiggXC5uF5V7ERBx\n4Ydg1cu9iuDK4gKCRUVQWRQs0ALaQrGFsoS0aZs0SbNPZl/O8/vjnJlMkkkyCU2TSb7v1ys9M+c8\n58wzZ/LkmZ7v+T5PrO8QfloPyHzqG5jqO1+U0+kgHA3gcjtoqdfk5rnsAFTfLCl3rpOcHCcO5+T6\nribBJTElpAsiOBwOzj//fL73ve+xadOmtGVS57hJlZhz5sMf/nDauY5OO+00ZsyYQXNzM6+99lpy\n+LKEI488kiOPPHLAfmvWrGHmzJns378/7X7/+te/eP7559m7dy9+vx+tNQBut5u2tja6uroGDHc2\n2PsHuOiii3jxxRfZtGnTuAWXPvrRjzJz5kyeeeYZ6uvrmTt3LgD79+/niSeeoLCwkAsvvDCjYzU2\nNlJfX49hGGn3cbvdfPzjH+eOO+4Y9DMfqcTvwmB1/PjHP542uPTXv/4VYNAhCZcvX47H42HHjh2E\nQqG0mXX9Pf300wCcddZZaYcYLCgoYMWKFTz99NO8+uqrnHLKKbS0tPD666/jcrkOyvkQQgghhBAj\n53I7WbC4kgWLrYyQaCRGQ30ne+vaaW7sprWlm3jURBkOdDK7KUY4HMMwIhiGQhkKl8uRnLPJ7Xbg\ncBpy0V6MqeLCUooXr+SoxSuT68KREI1N9XgKipLrmg80EAoH2LXnTXbtebPPMQryC/nWV+6j0GP9\nX7a5ZR8FBYV4Corl91cIIcR7opSy5mxyAK5hi1tD9Jl9h+lLBKNS54tKzCGF1sS1iaGgoyWaMkSf\n0Scbqv+wx4lsKJfbiTvHYd0oZGdMJTLUU7/TTdQbiCS4JKaEOXPmpF0/e/ZswApkpDNrVvpJSpua\nmoY8LsDcuXNpbm5Ols2kPok67d+/v0+dfD4fV111FU888cSg+wF4vd60waXRvv9Dwel0csUVV3Dr\nrbdy7733JocDvP/++4nFYlx00UUUFhZmdKzEuZ4xY8agwZhE8Crd5zIaiXM33Dnur76+HoCTTz55\n2Nfo6Ohg5syZw5bbs2cPADfffDM333zzkGXb2toA2LdvH2BlSyWG0BNCCCGEEOPL5XYy77BpzDts\nGgDvvPMO/p4oRryQxr1dtDX34POGiMdS5iCImUTDcYKBSPKihsNhpFykcOJyO2TuJjHmcty5zJ+z\nuM+6k973IZYuOY79zXtobNpNY1M9jc31NDbVY5pxPAXFybI//sWt7NtfR0F+ITMqZ/X5mTtrEWWl\nlQghhBBjQSmFw6FwOACGH/JOa01Pjx9tanJy3ClD9JlEIn2DU9o0QaVmQ1lLpfoGoBJZ6oayyqTe\nQNR3rig7KyoRrLKzo9w5TlwuxyGZO0qCS0IMYaJcbP/mN7/JE088weLFi/n617/OihUrKC8vT86/\ntHjxYpqbm5OZTNnm8ssv57vf/S6//vWvuemmmzAMg1/+8pfAyIbES8iGu9vi8TgA5513Hjk5OUOW\nHW57/2OuXr160KBWQiJwmg3nSgghhBBiqlNK4Slys2jRbJYdZ33PCwYi7KltY++uDtpaeujuChKL\nxtEm1lB6sTjRSJxwOJoMNimlcLkNK9Dksu6Kdbok4CQOjaLCUooKS1m8aHlyndYan787+f8SrTW5\nufnk5ebjD/RQV7+TuvqdyfJnfOBizjvjCgAa9u/ixS1/ZUblLKqmW8EnyXYSQghxKCWCUTgUuXlD\np0almy8qkZFuak08ZhJNZExp7G1WgEqplHmhDCOZIaUMa5g+lZoxZYDhMHA6DZwuB06Xgcvl4JgT\n51JSln9Q378El8SUsHfvXo4++ui06wGqqqpGdLxE+USmSDqJzJR0x068bjrp6vTHP/4RgHvvvZcl\nS5b0Ke/3+2lpaRmyvgf7/R9sFRUVnHvuuTz00EP8/ve/Jzc3l+bmZk466SQWL148/AFsiffR1NRE\nOBxOG5QZ6nMZjaqqKurr69m7dy/z5s0bsH2wz7q6uppdu3Zx3XXX9Zkb6r2orq4GrKH2rrrqqoz2\nqampAawhBYPB4IQJqAohhBBCiKHl5btZvGwmi5dZGe7xmEnTvi4a6jtobuym/YCfUCCSnGMgHjMx\ntSYSAUNFe++KNRROl3XxoX/ASS7Si7GmlEoOh5d4fsM1/4vWmm5vB80H9iV/mlr2MXfW4cmy7+7e\nyVN/39DnePn5hVSWV1FZUc2F53wOl9O60BcI+MjLK5DfaSGEEONmpPNFJVhBqd4MqD5zRMU1sWgM\nM56SzW5a5ZWysp+UYb324qUzJbgkxGhs2LBhQHAlHo/zu9/9DoCTTjppRMdbvXo1AE8++WTaeY6e\neeYZmpub8Xg8LF++fMD+r7/+Om+++eaAoMKmTZvYv3//gP06OzuB3uBBqkceeWTYjKUNGzZwxhln\nDFj/29/+Fhj5+x8Jl8tFNBolFovhdA7+J+fqq6/moYce4p577kkGhTINkCRUV1czd+5c6uvrefjh\nh7n00kv7bI9Gowf9Pa9evZr6+np++9vfsnbt2gHbN2zYkGYva16un/70pzz66KMHLbh02mmn8ctf\n/pJHH30043M3ffp0jjzySN544w02bNgw4Jyl43a7gd5MKSGEEEIIMf4cToOaeWXUzCsDrAsRXe0B\n9rzbRsOeTtoP+PD3hInHTTu7ySQWsx6Hw/S5+KAMhdNhJANNVuDJCkDJxXlxKCilKCkup6S4vE+m\nU6oFc4/g3I98iqYD+2ixg0+BQA/1gR4OtO3nE87eO8hv+/41tHceoLK8imkVM5lWMZPp9rKmah7F\nRWWH6q0JIYQQI2IFpRRpplcfVCJLStuBJlNbWVIHmwSXxJRwzz33cPrpp3PCCScAVgO7/fbb2b17\nNzNnzuSss84a0fFOPPFEjjnmGF599VX++7//m7vuuisZENm/fz833ngjYAVH0s39o7Xm2muv5aGH\nHqK42Bpbuq2tjRtuuAGAyy67rE8GyaJFi9i5cyf33HMP1157bXL9tm3b+OY3vzlsfR977DH++Mc/\ncvbZZyfX3X///WzatAmPx8MnP/nJEb3/kaiqqmLv3r28/fbbHHnkkYOWW7FiBatWrWLLli3J/dIF\nxIbzuc99juuuu47bbruN448/nsMOOwywAiFf+9rXaGhoYNasWX3OxXtx1VVX8Zvf/IaHH36Ys88+\nmw9+8IPJbXfddRfbtm1Lu98111zDQw89xB133EFFRQWf+tSnBgTf3nzzTWprazP+/TzzzDNZvnw5\nmzdv5ktf+hJf+9rXKC0t7VOmpaWFJ598kssuuyy57vrrr+fSSy/llltuYebMmZx55pl99tm2bRuV\nlZXJ4GYi62vXrl3DBg2FEEIIIcT4UEpRWlFAaUUBy4+35geNRmI0NXSzf08XLU1eOlv9+H1hzLhp\nDdNiT2KtYyZRHScUiqZc0LCWTldv0MnltIZacTgNCTqJQ25W9QJmVS9IPtda4+3p5EDbfvyBnj7r\nQ6EAkUiIhqbdNDTt7nOcsz58KWd/2LrJbteet3j+pT9TXjad8tLpVJTNoKJsOiXF5dad5kIIIUQW\nSGRJkTL0sRpBcCpTckVQTAmXXnopZ5xxBieeeCIzZszgX//6F7W1teTl5fHTn/50VEOB/fznP+ej\nH/0ojzzyCJs2beKEE04gEAiwadMm/H4/a9euTQaL+jv99NN58803WbFiBSeddBKxWIxNmzbh9Xo5\n5phj+MpXvtKn/PXXX89ll13GLbfcwu9//3sOP/xwmpqaePnll/nYxz7Gyy+/zL59+wat69VXX81l\nl13GqlWrmDNnDu+88w7bt2/H4XDw/e9/nxkzZoz4/WfqzDPP5O677+bss89mzZo1FBQUAHDnnXem\nrWciuHTZZZeNKmjx7//+7/zjH//gkUce4aSTTuKkk06itLSUV155hfr6ekpKSvjFL36R8TxGw1m+\nfDlf/epXueWWW7jwwgt53/vex6xZs3jjjTd46623uPrqq/nJT34yYL+amhp+/etfc9lll3Hdddfx\nP//zPyxevJhp06bR3d3Nzp07aWho4Lzzzss4uGQYBg888AAXXHAB9913H4888ghHHXUU1dXVhEIh\n6urqeOutt5g2bVqf4NJZZ53FjTfeyO23384nPvEJlixZwhFHHIHP56O2tpZdu3bx+OOPJ4NLs2fP\nZunSpWzfvp3Vq1ezbNkycnJyWLRoEddcc81BOa9CCCGEEOLgc7mdzJ5fzuz55cl1sUicpoYumhq6\naG/109UeoLszSDQSt+56te94jcesu14jYZIZTr2TUFsTTaeO6+90OqxJqCXoJA4RpRTFRWXJLCS/\n359c/71vPkQg4ONA+35a2/ZzwP5pbdvPrJm9Aao9+97hhZefGHBsh+GgtHQat95wLy6XNZLD629t\nxeV0UV46ndKSaTgcEnwSQggxtUhwSUwJt912GwsWLOC+++7jlVdeIScnhzPOOIOvfOUrQ2bTDGX+\n/Pk8//zzfP/73+cvf/kLf/nLX3C5XCxevJiLLrqIyy+/HJcr/URuJSUl/O1vf+OWW27hr3/9K+3t\n7VRVVXHVVVdx7bXXJgMwCWeffTaPP/443/nOd3j99dfZvXs38+fP5/bbb+eqq65i2bJlQ9b105/+\nNKtWreLuu+/miSeewDAM1q1bx3XXXZcc4m+s3HzzzSil+NOf/sTjjz9ONBoF0geX1q1bB1hD6V1+\n+eWjej2lFD/72c847bTT+MUvfsHWrVsJhULMmDGDK6+8ki996UvJeYYOlmuvvZaFCxfywx/+kO3b\nt7Nz506WL1/OH/7wBwzDSBtcAlizZg0vv/wyP/3pT3nqqafYunUr0WiUyspK5syZw5VXXsk555wz\norpUV1fz7LPP8qtf/Yo//OEP7Ny5k61bt1JWVkZVVRWf//znB2QmgRXAPP744/n5z3/Oli1beOyx\nxygqKmLOnDnccMMNHHXUUX3K/+pXv+Ib3/gGmzdv5ne/+x3xeJzVq1dLcEkIIYQQIss43Q5mzS9n\nVkrASWtNR5uf5n1dtDb76Gzz090VJODrHVZPJ7KctImOaCKhGMpIzXKyJpN22QEnZzLLyYFDgk5i\nHOTne5ibfxhzZx02aJnFi5bzyQu+QFtHM20dLbR3tNDe2UK3t4Ng0J8MLAE8+Ls7aWltBKwb/UqK\nyiktmUZpSQWrlq9j5fI1AITDQfyBHoqLyiUAJYQQYlJRw83VIg6t7u7ujcDAiVvSSGSqzJo1awxr\nlJ1CoRBAMiOnq6trPKsjMvSjH/2IG2+8kXPPPZf77rtvvKsz5STaTbqhHA8W+bslJpva2lrAGr5U\nCJEZaTdCjNxEaTfRaIy2Zh9NDd20NffQ2e6npztEKBi1Ak12lpM2rSH20L1ZTonhWZRhBZ+cTgdO\np4EjEXhyWsPrJbKhhHivEplL/W/eHI1oNEJ3TycVZdOT6+598Lu0tDbQ3tFCl7e9z1zI537kU5z5\nwUsAeO31l7jz5zejlEFxUSmlxVYAqqykktKSCtat/ii5OdZoKvF4XAJQYlwdzHYjxFSRLe3mhFMW\nMHN2KcBzxcXF6w7GMSVzSQgxIXi9Xn74wx8C1rxJQgghhBBCiInF5XJSNauEqlklfdYHAxGa9nbR\nst9L+wEfXR0BfN4w0WgsZTJprABU3ESbmrCKWdMApAyvl8h2cjoNa4g9O+BkLR0YhgSdxPhwudx9\nAksAV1x8XfJxNBahq7udzq42OrtaqZ45L7ktFotSXFSOt6eDru52urrb2b239zgnn9Q7DPr/3H0d\nexvrKCkqp7i4jOLCUoqLyikuKmPenMUcvmApQDKQJYFYIYQQ40mCS0KIcfWDH/yAnTt38uKLL9LY\n2Mg555zDypUrx7taQgghhBBCiAzl5buZv7iS+Ysrk+u01nR3Bmna10VbSw/dHUG83UH83jDhcCwZ\ncEoMr4c2MTWgY72ZTv2ynhwOA8eAoJOB02FgOMZglmohMuRyuplWXsW08qoB21YuX8PK5WuIxWN0\ne60AVEfnATq72+jxdZHj7h05osfvJRjyEwz5aTqwt89x1q3+aDK4tKehlm//4IsUF5Yl55lK/BQV\nlnLs0vfjKSgCrOCWw+GUQJQQQoiDToJLQohx9dRTT7F582YqKiq47LLLuPXWW8e7SkIIIYQQQoj3\nSClFSVk+JWX5A7aFghFam320tfTQ0erH2xmkxxsi4AsTi5qYOmV4vcS8TnbgCaWSGU/953dyOKxg\nk7VUOBwGhmHgcCgMhyGZT2JcOR1OykunU146Healn/v5lut/hj/gpcvbQbe3g+7u9uTjRQt658H1\n9nQSjUbsuaGaBxxn8cLlyeDSPQ98h1e3b6KwsIRCTzFFnhI8nhKKPCXMrlnICStPA8A047R3HqDI\nU0KOPUyfEEIIMRQJLolJTeZamvj+/Oc/j3cVhBBCCCGEEIdQbp6bWfPKmDWvrM96rTW+nhCt+3to\nbemhsz1AT1cQvy9C0B8hHjOtoJOd8aS1Jh7T9vxOMTvg1G+OJ3uZGH7P4TAwHClLwxiwTjI8xHhR\nSuEpKMZTUExN1bxByy1d8j7uWv+4FYDydtDtbafb20m3tx2vr4viot62FQz7icWjdHa10tnV2uc4\ny486IRlc8vZ0ccP/+yQAblcOhZ4SPAVFFBQUUZBfyEdOvYjZNQsBaGjaTXtHC56CIqtMfhH5eR4M\nQzIIhRBiKpHgkhBCCCGEEEIIIcadUorCojwKi/L6DLEH1rxNPd4Q7Qd8dLRa8zp5u0L0dIcI+CPE\nIvF+gSeSw+0l1kFvwImUwFNvAAoUKiXQZGc99ct+MgyVDEJJIEqMl9ycPHKnVTN9WvWQ5b74H7cR\njoTo8XXj83Xh9XXR4+umx9dJedmMZLlwJEhZaSXenk4i0TDtnS20d7Ykt5+8+qPJx5v/+TRP/31D\nn9dRSpGf52FW9QKu+9z3kut/96d7cDndeAqKyM/3kJ/X+1NaUkFebsF7PRVCCCHGiQSXhBBCCCGE\nEEIIMaEpQ1FUkkdRSR7zDpvWZ5vWmqA/Qnurj862AN2dQXzeEH5fmKA/QigYIxKOYZqJ4fV6M59M\nE7Q27XWg0VbQCJIZT8mAFKmBKexh+YxksCmRGaXsAJTDMFD2+sSPBKPEeMhx55JTlktF2fRBy0yf\nVsN3v/4gWmtC4SA9vi78AS8+vxd/oIeZM+b2lq2o5qjFK/EHepLbA0Ef/kAPwaA/Wc40TZ545mGr\njaVx8Xmf49Q15wKwZdtG/vCX+8jP85CXW0Benof8vIJkIOr0Uy/C4XAAVuaUwgpm5ebmk+POlawp\nIYQYBxJcEkIIcUhYd4sKIYQQE5dpmrz77rs0NTURjUZxuVxUVVWxcOHCCXXRKhKJ8MADD7B9+3aC\nwSB5eXksXbqUSy65BLfbPd7VA7LjXGZDHWOxGM8++yybN28mHA5TXV3N4YcfzimnnILTKf+dT1BK\nke/JId+Tw6x55WnLxGIxdmx/i/q6Bnq6w8Qi4HZ6yMspIhyMEQpGiYTjxGK9GVCkZkFZkSfQGk1v\nhpQiJespkQGVWEdKMMp60jfQ1O+xArp72vH5u4mZERyGg+KiEiqepKWPAAAgAElEQVSnVVtBKwlM\nZcQ0TVpaG2huaSQWj+Ep8FBSXM70aTUTpm2D9Tu5851XaGreSyQaxu3KoWrGbJYcduy4tm+lFHm5\n+eTl5gMz05ZZt/pM1q0+s8+6eDxOINhDNBpJrjO1yQVn/UcySBUM+gkEfQSCPoJBP8VFve21y9tB\nS2tj2tdzGA7O+MDFyec///W32ddY11tnFC6XG5crh6VLjuOMD1zM9Gk1tHU089iTvyQvt8DK9MrN\nt35yrPd3xGErkplTgaAPpRQ57ryD/nuS+J3s6m4nFo/idLgm5O9kNpBzKcTEMqm+jSqlLgY+AywF\nHMBbwH3Aj/Rgt0kMfbwPA9cCK4FcYBfwG+B7Wuvwwar3e6W1li+ZQgghhBBCjFIkEmHLli1s27aN\nxsZGurq6iMfjOBwOSkpKqK6uZsWKFaxatWpcgzcdHR2sX7+e5557jtbWVkKhUPL/Ao899hg/+clP\nWLt2Lddffz1lZWXDH3AMZMO5zIY6+nw+HnjgATZu3EhDQwMdHR2YpklOTg5FRUXcd999rFu3jksu\nuQSPxzMudcwWmX/ex+N2u4lF43i7gnR3BfF1h/F5g/R4wwQDUSKhKOFQjHAoRjTSG4hKZj3ZN1Ml\nh+QDa1g+ex320Hy9wSbrorhGEwz5CIX9RKMR4mYc0CgVx+/toLXFT35eAZ6CQhwOR/rglOp9nnys\nFMpIZFilZF5NUrFYlLo9b1K/9x06ug7g9XZimiZut5uC/EJKSyqZO/swFsw5AqfTNW71DIUCbPrn\nU+x8+1U6ug4QCgUwTRPDMMjLzWfj5j+x5PBjOOm4D5Gbmz9u9Rwph8NBoaekzzqnw8mHTj4/o/1P\net+HOXrxqt7gUygRiPITi0X7/O5WVswkFo3g9XURCgeJx2NEomEi0TB79tXy3It/orSkEsMweGnr\n3wZ9zVtvvDcZXHrgkTt5+ZVnAMjJySMvN58cdx45ObksmLuET5x/DWD9nv3mD3db2WDuXHJy8pKP\n3Tm5LJizhNKSCgC8PZ28s2sHTS378PZ0Egr5k5/1RPqdzAb923cg0CPnUogJYNIEl5RSdwGfBULA\nM0AUOBX4IXCqUur8kQSYlFJfBtYDcWAj0AmsBW4FzlRKnaq1DhzUNzFCDoeDeDxONBqdMHcoCiHE\nYKLRKEByKAMhhBBiIvD7/WzYsIEdO3awb98+TNOkoqLCusgci1FbW0tdXR27d++mtraWCy64gIKC\nQz8/xJ49e7jiiiuoq6vD7/ejtSYnJwfDMNBa093djdfrpbm5ma1bt3LvvfcyZ86cQ1rHbDiX2VDH\n1tZWbrrpJrZv305bWxumaZKbm4vT6URrTUNDA/v372f37t288sorfOtb32LatGnDH3gKGu3nXTbN\nQ9m04YN2sUgcX0+IHm/YGoavJ4zfFyHoDxMKRAmHY0TDcSKRGNFonFg0jjUCX29mVNyM093dRigc\nIBKx7mF1OJwoFKbWRCIBgqEgwUAAv89PcWE5hsO6O793qD4YkC1lreoTxFLKGl4wMVeUFYhi2KBU\noryyyxspc1ZNFOFwkJdfeYZ9jbto72zBNE3ycj04nC601jS17KOltZHWtv00t+zl+GNPJScn75DX\n09vTycOP/pi9jXX09HSitSY3Nx+Hw4lpxunobKWzq43W9iZ273mLC8/5NEWFpYe8nuOhN1tqeFde\n/OU+n3c8Hic/z/pbnfp5ewqKWX3cB5k5Yy6xWJRQOEAwFCAUDhIK+fEUFCWPaRgOcty5hCMhwuEg\n4XAwua2woDj5OBQOsHHz44PW7dOX38yq5WsJh4P86rf/x6s7Nie3KaVwGE57HjcHi+Yfnfyd3LXn\nLcKREG5XDi6XG7crB7c7B7crh4Xzj+LwBUsB63do1563cNuZWqnlXe4cCguKMIzJ9X/udO270FOM\n0+kiHo9NmPYtxFQ0KYJLSqmPYQWWmoE1Wutae/104O/AucB/At/P8HgrgW8DAeAUrfU/7PUe4M/A\nGuBbwJcO7jsZmdzcXPx+P8FgUIJLQogJLxi0vpzn5uaOc02EEEIISyQSYcOGDWzZsoXm5mYWLFhA\nSUlJnwums2fPpquri7q6OkKhEAAXX3zxIf3+3dHRwRVXXMHbb79NKBSiqKiIvLy+w/aYpkkwGMTr\n9fL2229zxRVXsGHDhkOWwZQN5zIb6ujz+bjpppvYunUrXV1dVFVVUVRURDhsBR3y8vIwTROv10tT\nUxNbt27lpptu4o477pAMpn4OxeftdDsoKS+gpDyzAKTWmmAgQqAnQsAXprvbz9NP/43Wxl34vD7K\ny2eQ684HHQcMlDZw5+Rhxk0ikQjhKPhCBqVFFShloLGzpgDSDN1nvWbva6t+WVPWQvU+7hekstYN\nDFTZe9kBJ3qDTylDA6YGo/puS5nDKs26/vNcqQyCWLFYlJdfeYa6+jfp9rYzfVoN+XkeorEYAG6X\ni4qyGQSCPlpaG4hErfa0+rgPHdIMh1AowMOP/phde97EH/BRWlxOXm4BKuVvuTZNgiE/nd3t7IpF\nePjRH/PJC76QVRlMY22wzzv190Rrnfy8i4vKycvNH/bzvvKSL3PlJV/GNOOEIyGCoYAVZIqEcDl7\n/ya4nG4u/tjnCYdDRCIhKxhl/0QiIcpLpyfr2NHdhtMOcJqmlekYi0chDjlGHtPKq5K/k69u30Qw\n5E9btzM/eEkyuFS/7x3u/PnNg76P73z9AcpLrbm1fvqr23jz7Vd7g1BuKwjldLpYOO9Izv3IpwAI\nhvz89o8/sc6PVjidLvLzCnA6XTidLpYfdQLTyqsAaG7ZR0tbIy6nC6fTjctlLx0u3O4cykork3VJ\nZBa9F5l83hOhfQsxVU2K4BJwo728PhFYAtBatyilPoOVeXSDUurODLOXbsD6yrQ+EViyj+dTSn0K\nqAU+q5T6pta666C9ixHKy8vD7/fj9XpxOBzk5+cnv5gJIcREkJgoORAI4PV6AetvlxBCCDERbNmy\nhR07dtDc3MzSpUvTXlBWSlFaWsrSpUvZvn07O3bsYMuWLaxevfqQ1XP9+vXJi98VFRW4XAMvlhiG\nQUFBAW63m7a2Nurq6li/fj3r168/JHXMhnOZDXVMzKXV1dXFggUL0tbRMAxKSkrIz8+nrq6O7du3\n88ADD3D11Vcfkjpmi4n4eSulyC/IIb8gByhk8+a32d+2k5bOeruOYN3jOlA4FOH113dSUz2X5Ued\nxmELlhAMRgkGooSDUSLhGNFIjEgkbg3ZF40Ti5rEonHicZN4zLSG7usXkIK+w/lBSpAKksP6pW7H\nPo6dN5UmYNW73nrfyTPQ73m/wFHvLn2CWAwIUNnb7LmuOrtaIVbAjLLDOGx2CcrO6IzFY2ht4nAY\noDWlhZoZ5QtobW/C3xNh1+5dVFfNTc6HlZr5NdzcWarf4wHvJY1N/3yKvY11+AM+pk+bidOZ5nfS\nMMjPL8TtzqGldT97G+vY9M+nOG3NuUMeeyqp2/Mm+xp30e1tZ3b1wrQBBKUUBfmFzK5eyN7Gd9nX\nuIu6PW8mAzRDMQwHebkFyeHy+svJyePU958z5DHertvOvsZdePIL+eDaj6UEmEzi8VjydzO1jgvn\nHcWcWQupKJtBJBomGg0TiUSIRsMcllLvgvxCli55nzUMYCRMNBrpLR+N4Hb13szp83Xj9aW/bJmb\nktkTDPp5/qW/DPp+KitmJoNLL73yN/709ANpyxUXlXPHLQ8nn//X1y/E5+/G6XTjdLpwOd04HA6c\nDhcfWHsep7z/bABqd+3gD3+5H4fDidPh7LP0B3ooKSpPft77W/ayr7EOZRgYysCwl8owyM/z0O1t\nZ1/jLt6q+xfxWKzvMZ1OHIYTp9NFWWll8hyEwkFisQiG4cBhODAc9nKSZYAJMRayPriklKoBjgUi\nwIb+27XWzymlGoFq4HjgxWGO5wZOt58O+Guptd6llHoJWA18BHjwPb2B9yAvLw+Px4PP56Ozs5PO\nzs7xqsqEY5pWDFEm8xMic4ei3Xg8HgkuCSGEmBBM02Tbtm3s27dv0Iv4qdxuNwsWLKC+vp7XXnuN\nE0444ZB814xEIjz33HP4/X6KiorSBpZSuVwuioqK6Onp4fnnnycSiYx51k02nMtsqGMsFmPjxo20\ntbVRVVWVUR2rqqpoaWnhueee48orr8TpzPr/4h8U2fB5j7SOOblu5i+YQ339bhpb3uGs804dUR21\n1kTCMYKBKKFAhGDQmj8qEooRtueSikTiRMMxIpEYsYhJNBonGo0Tj6UGqawL5Kapk0Em6wX6BqwS\nr5l8nPKPmXrLb0qWVZ/jJB/rAcEq+1nyua8niEPlUlFSjMPR2wYSr68M1bsPisI86+J90Bens82f\nPijUJ1BGvyeKtGEk1ZsJlhqcUsoO2EULWHbYKbhcbhwOJ1qbaG1i9llqrHuiNXOqggSCPrxdAbo6\n/Nbw4n0CcKpPMC4R7Op/fgZmp/XWre+pVUMev89D1Xdl2lM4Bjc+m6ZJ/d53aO9sYfq0mmEzU5xO\nF9On1dDa3sSefe+waN5Rh6Rtp6ujUgqHw4HD4cBNTto6FuQXsvq4Dw1ZxwVzl/CF//hWRnX57BXf\nIBwO2sGnCJFIiGgsQjQWpSC/MFkuL8/DpR//ItFolEDQRywWA6WJxaLEYtFkYAlgekU1Rx9xHNFY\nhFgsSjQWJWY/7j/nVjwewzRNInZWV6rULK1ubydvv/uvQd/HksOOoWr6bJxOF41Nu2ltb0pbbkbl\nLI48/Fha25uordsxaBAM4ItX38bRRxwHwF/+9hv+/NeBl3eVUlSUzeDbN/8que6rt11BIOTHYRh9\nglAOw8Fpa8/j/cdbl5TfqdvBH5/8ZZ9yDoczWfYTF3whOQzks5v+SMuBRuv3ww5uJcpVTZ/Nscve\nnzxnL/7zaTuw5rACa8kgm4PFi5ZTUlwOwP7mPRxo298n+JYIxrndOcybvTj5nhqadoPWGIYjpaxC\nGQ4K8j3JQGssFiUcCfV5zdTjiqlpMnzzXGEv39BaBwcpswUruLSCYYJLwOFAPtChta4b4nir7eON\nW3AJoKSkBLfbjc/nIxqN9vnyNpVFIhFAht8SYiTGqt0opXC5XHg8HvLzZTgHIYQQE8O7775LY2Mj\npmlSUlIy/A5Y371N06ShoYG6ujoWLVo0xrW0MllaW1vRWmd8g0ZeXh5er5cDBw7w4IMPcvnll49p\nHbPhXGZDHZ999lkaGhowTZOioqLhdwCKiopoamqioaGBv//973zgAx8Y0zpmi2z4vA91HZVS5OS6\nyMl1Qdl7/05uxk2ikTjhSIxIOE40bAWoonbmVDRizzUViRO1M6iS2VSxOLGYlU0Vj5lW0CpuYsZ1\ncpkIYPUGsYCUQFZiEQ4HicWjKMWAQEPi6oiyH1uxLesCqtaacCRMMBQgx5VHv1foc5B061LCaqSE\ncwYGYewHPn83DiOX4sJKcty5fQv2l9iktTUkm8tN0/4WPAUlfcoMF7pRmRTqV+c0TwdZqQbf1G/D\ncMHBxJqB63qDdAmBYA+enCqOmOehuLAUlO7NqEt+hv2ClSWakoLZ5DqKaNjbjMfTO3/SMG8tzVtK\nF3Xsy9vTiVMVMnvG0ZSXTe9TVA/4bbJ+wUo8GrejBMPMp7GhieKisvQBzrS/YENVR+EgnzxXPnku\nrKudKXw9iYCPg2OPtvqPsD1EaE5ubp/j+nus4eaWHbGWZUesHfQVE+UAbrvxN5hm3A5CRYjFo8Tj\nceLxGPl5Hvw+q2xN1WI+f8VtVjAqHrfLxfD2dFLfUEthQSmVZXNQSrFw7jJmTJtjZYGZcbRpYppx\nTG1SWjyNaWVziMccmFGDRfOWYhgGcdN6zUTWWDweQ2k3Qb91DQTTID+v0DqOGU+Wt7LNrOFME7q8\nHQRDvrTvvbOzI1m2te0Ab9VuG/Q8fewjV6O09Tdr67YXeLvutbTlVhx1EkcedjwA7R3tPPj7uwY9\n5uev+BZHLLK+Pzz/0pP89bkBORgAlJdO55Yv3598vv4HXyIQTP+ezvrQ5Xxo3YUAvLrjBe558LZB\nX3/9Vx9OzmP2419+k9pd2zEMA6UMOyPUClodtfg4Lj7vC4CVefp/P7seQxl2YN4qa9jLfzv3P5k3\n+wgAnnvpcf657ZkBx1PKoLiojMsv/HKyLvf+5nbCkVCfMol9Vi5fx7IlJwBQv+9tnn/5T31eUxmG\nPfSrwbkfudL+mw0v/OMvtLbvTx7HmstQ2UHImSw/cjVhhxWgff7lP0HK9t5haRUrjj4pOXRlXf0b\n7G181w7OpWbNKvJy81m5bF3yPW15bSPxeNTanlJHpaC6aj5VlbOtc9rdSv2+d5Kvm5yf0TA4ZvVM\n4ODO4zcZgkvz7OWeIcrs7Vc2k+PtHaLMSI6HUupy4PJMym7cuHH58uXLCQQCNDY2ZrKLGEJi3Gwh\nRObGot0k5oAQYrKqra0dvpAQoo/xbjdbt25l7969uN3uEY0A4Ha72bt3L1u3bh3D2vV64YUXCAQC\nOJ1O+4JMPKP9nE4ngUCAF154YcyHdMuGc5kNddy8eTMdHR3k5uYm51jqLzGHZarc3Fza29vZvHkz\nc+fOHeNaZods+LyzoY6j4gaXG/pexzbsn5HPf2IFmSAWNTHjJrEYxCIm2jSJxTRvvP46O3ZvBQ3l\nuZWglfWj7KWm9zH2j1b0hLpRYQfllXmUTStBazBNa0hvbYI2raCFmXiu7SCG1ph2pCq5Dgbe6Ns3\nvkEkGsQ049YFRJVSIN39wSnrDMMgHo8TCgXIzytMUzjx+iM7r2mDZgen8AhkFB3pIxAMobQbT34Z\nhmFl/2SSIFVS6EKh8HlDmLGxmYcnEQfzB8Lku8vIryjrM1fTcNyVRYDC1x3GjCYu9B/87K9M+bzR\nQbeNqlbKADtjywGE/RD299gbDco98wfs4i/yUlZorXe7rH1XLJ417Et5cmYAsGTB+ynIH/xmjdYW\n6xrFyiPPZOWRZw7YrrWJaZq0Nvdey/jcJ/4nGcxKBKKsoJSJp6A4Wba0YA6fPPcm+29YzF727tfd\nEcHX3Q3AssNPYc7Mo1PKxJP7TSubxYEmq5w/EGPV0g9aWY5mb9Zj4nE87E6WzXeVs2juiuR70Ohk\nucKCkmQ5gPKSagry/L0ZlHZ50zSJhY1k2Z6uEDnu/D7lEnUA6Gj1EfBafyx6enoIhdMP89rZ2ZU8\nZkdXB20d6TPRAFqa2ylwWWUbGvZRv+/ttOVKiyr7vKfX39pKOJL+9cuKaqgqXQLA7l27+cerfxv0\n9U9Ydi65OVbm1stbnmV3wxtpyy1ZeDzzZ67C2xmho6uZx576xaDHLHBPZ/5sK2D10j+f48VXHx/0\nPc2atiL5/MHf3znoezr1xH/jpJXWMJOvv7OV3z35g7TlLvjkycxj5qB1G43JEFxKzFqaftY7S+Kv\n8uA98dgdD2AuMHhYP/XAvvSRYiGEEEIIIcTBE41ad8+OdMg4p9NJJBJJZvyOtVAohNZ6xMONGIaB\naZppgxEHWzacy2yoYzgcxjTNEQ9t53A4iMVicmNdimz4vLOhjhOBNewTOJ3p/wbW7Y0TMbtwu904\n8zL/excJtBCJRJg+/zBOPLF61PVLBqFMEzMOcVNjxq3HpqntLCzNI49s4p9v/B2X001ZaTnW/ev2\nHfqGFXyz7kA3UHZwTCmFr8eHRrO0+BhmL1zUGwDT2D9W4MdMCYAlgmB9HifqCnZgLDVgljIXV7/H\niahVcr/kk8SmvvN1Dcgyy+gkZr5ZGRqldDIbIVOGYVgXwA2NYYxBwEb3f6JRGJlFvmwKq47WLGeD\n7TcxRisarhZ6wIMMdkrDNK2hIg1ljHikpsQcV6b5Xs6ZQilHn2Pk5Q6dWZwom59bzNzq4ozKHj5/\nVUbl8nIL+fCaT2VUdunitSxdPPil6NT3dPnHvpFxPb/8H+nragWYVLLshWf8N6YZTw71mZiP25oH\nz5UsV1hQzuc+8b/WNuy5ARPl0ZQWVSbLHnvUBzh83kqrhaUeExNnyjEBzvvQf6a8vl0HrMeV5bOT\nZWdUzuesUz894HiJv4+G0XvcFUeeyvzZy/ocD3ufirLqZDm3K58TjznLOi8pZcA6ZmFBebJs9YxF\nrDz6g/Y2nfw911rb2XS97+nIRScQjUX6lbWW5SUzk2U9+aUcPn9l8lzaB0SjyXEd/BG+JkNwKRvU\nA89lUtDj8SwHivPz8w/JMBuTVeJOWDmHQmRO2o0QIyftRoiRmyjtZv/+/ZSWlqK1pqysLOP9vF4v\nBQUFzJs375C8h+nTp1vzbMCw8y2lSsztMGPGjDGvZzacy2yoY3V1NTk5OWmHQEwECdMNjWgYBjk5\nOdTU1Ix7u5oosuHzzoY6ZoOhzmNHRwdA2vN7qM/jlm3PEdvoJxr2Uea0croSQ/WlTkGVvABvb2zu\nbEApxdzFazj/srHNQj0YeoNdJtrEytLQdmArJTBmxrWdGWHP/ZsI0NnvO7FOm9qar8rOInvllS08\n+dSLaA1VFVUkgzCpiWCa5PrE87YDTRjKYOXRc1my5MjeutI/KEfKukQwLiWAlvK492nqBWF4++2d\nNG7ZiwYqCivsM2MNzth7mbhf8EhDj78dZSgWz6lm3rzZyQ39s+MGBPL6rO99hdRYTP+hA/tv712n\n6emxsokKCwvTlNMDHg44TL/6Dmao7YlNDY1BWrraQGuK8krSloG+84QBBINdoBRzps2gumpaStUG\n1n/QOgxVsUEKDHrI5LnSg6w/CEZ0kNG9Yr9fsYNmFtOGLwTMzGA4t0T1qmrWZXTMKkpYsuSwzMrW\nnD7otr7f00pYsOgzGR1zRs0HWEdmQxpf+cn/zvCYx3Pcccen3TZ9elXa9e/FZAguJVJ9CoYok8hG\n6hmizFgdD631/cD9mZTt7u7eSIZZTkIIIYQQQojRqaqqoqSkhNraWmbPnp3RxONaa9rb21m0aBFV\nVQf/P2fpLF26lMcee4zu7m5M08wog8k0TcLhMMXFxSxdunTM65gN5zIb6nj44YdTWFiYnIcn08+6\np6eHmpoaDj/88DGvY7bIhs87G+qYDbLlPE6V9q2UNa+Iw3DYaxxDlh+pUGw+/3w1n9raWuYumJ7x\n593x7j4WLVrEsScuYtGi4YdVey+mzdLU7nuZ2tpa5iwqyriO7+x9h0WLFrH29CXjGjieKDcBAbzz\nTiH779tCbW0t1YuOyfhc1jZuZ9GiRZx+/tET4n2IyW8itZtDbWRjK0xM9fZyzhBlEj1H/RBl+h9v\n9hBlRnI8IYQQQgghxASzcOFCqqurMQyDrq6ujPbp6urCMAxqampYsGDBGNfQcskllzBt2jSUUhkP\ncRcMBlFKUVlZycUXXzzGNcyOc5kNdTzllFOoqanBMIyM56r0er3JOp588sljXMPskQ2fdzbUMRtk\ny3mU9n1wZMPnnQ11zBZyLoWY+CZDcGmbvTxSKTVwjADLqn5lh/IWEATKlFKD/RU6bgTHE0IIIYQQ\nQkwwhmGwYsUKZs2aRV1d3bDzl0QiEd59911mzZrF8uXLRzwH0mi53W7Wrl1LQUEBXq+XaHTwCbbB\nmsclMdzTmjVrRjyfy2hkw7nMhjo6nU7WrVtHRUUFTU1NGdVx//79VFRUsHbt2hHP1TSZZcPnnQ11\nzAbZch6lfR8c2fB5Z0Mds4WcSyEmvqxvZVrrfcCrgBu4oP92pdRaoAZoBl7K4HgR4An76SVpjjcf\nOAGIAH8edcWFEEIIIYQQ42rVqlUcffTRzJgxg+3bt9PZ2TlgDgCtNZ2dnWzfvp2qqiqWLl3KqlVD\nT7x8sF1//fUsWLCA3Nxc2tra8Pv91nwUKUzTxO/309bWRm5uLgsXLuT6668/ZHXMhnOZDXW85JJL\nWLp0KSUlJdTV1dHV1ZX2s+7q6qKuro7S0lKWLVvGJZcM+K/rlJcNn3c21DEbZMt5lPZ9cGTD550N\ndcwWci6FmNgmy60PtwMbgPVKqRe11u8CKKUqgbvtMt/WWid7baXU54HPA//UWl/a73jfBs4FrldK\nPam1/qe9jwe4Fysod7fWOrOcTCGEEEIIIcSE43a7ueAC6/60HTt2UF9fj2malJeX43Q6icVitLe3\nYxgGc+fOZenSpZx//vmHJBsoVVlZGffeey9XXHEFdXV19PT04PV6ycnJQSmF1ppwOIxSCo/Hw8KF\nC7nnnnvSTmI/VrLhXGZDHT0eD9/61re46aab2L59Oy0tLTQ1NZGbm4vD4cAwDHp6ejAMg8rKSpYt\nW8att96Kx+MZ/uBTTDZ83tlQx2ww2Hl0u904nU68Xu+EOI+Dte/CwkIcDgfxeFzadwayod1kQx2z\nhZxLISY21T/am62UUncDnwFCwN+AKHAqUAQ8CpyvtY6nlP8G8HXgOa31ujTH+zKwHogDzwJdwFqg\nEvgHcIrWOnCw30d3d/dG+3XEezCVJ1ITYrSk3QgxctJuhBi5idhuIpEIW7ZsYdu2bTQ2NtLV1UU8\nHsfhcFBSUkJNTQ3Lly9n1apV43qxoqOjg/Xr1/Pcc8/R2tpKKBRCa41SitzcXCorK1mzZg3XX3/9\nIQ0spcqGc5kNdfT5fDzwwANs3LiRxsZG2tvbMU2TnJwcioqKqKmpYe3atVxyySVy4XkY2fB5Z0Md\ns0H/87h3717i8TilpaUT6jz2b99erxfTNDEMQ9r3CGRDu8mGOvY3Eb+nQXaeSzF1TNR2M4TniouL\n1x2MA02a4BKAUupi4HPA0YADa/6ke4EfpWYt2WW/wRDBJbvMh4H/AlYCucAu4EHge1rr8Fi8h+7u\n7gageiyOPZUEAlbcLz8/f5xrIkT2kHYjxMhJuxFi5CZyu9FaEwwGiUQiyaCN2+0mLy8PpdR4Vy/J\nNE0OHDiAz+dLXpD0eDxUVlZOmPkFsuFcZksdOzs7kxefc3JyyMvLo7S0dMLUMVtky+c90euYDRLn\nsaenB601ubm5E/I8Jtp3MBhMXiSX9j1y2dBusqGOCRP5e9TSqNoAABOWSURBVBpk17kUU8dEbzdp\nNBYXF9ccjANNquDSZNDd3d0FFI93PYQQQgghhBBCCCGEEEIIMal0FxcXlxyMA02WOZcmk93APMAH\nvDvOdclar7322nKfz1fs8Xi6ly9f/tp410eIbCDtRoiRk3YjxMhJuxFi5KTdCDFy0m6EGDlpN0KM\nXBa1m4WAByv+cFBI5pKYlJRSG7Hmrhp02EMhRF/SboQYOWk3QoyctBshRk7ajRAjJ+1GiJGTdiPE\nyE3ldjMxBuQWQgghhBBCCCGEEEIIIYQQWUGCS0IIIYQQQgghhBBCCCGEECJjElwSQgghhBBCCCGE\nEEIIIYQQGZPgkhBCCCGEEEIIIYQQQgghhMiYBJeEEEIIIYQQQgghhBBCCCFExiS4JIQQQgghhBBC\nCCGEEEIIITImwSUhhBBCCCGEEEIIIYQQQgiRMQkuCSGEEEIIIYQQQgghhBBCiIxJcEkIIYQQQggh\nhBBCCCGEEEJkzDneFRBijNwPbATqx7UWQmSX+5F2I8RI3Y+0GyFG6n6k3QgxUvcj7UaIkbofaTdC\njNT9SLsRYqTuZ4q2G6W1Hu86CCGEEEIIIYQQQgghhBBCiCwhw+IJIYQQQgghhBBCCCGEEEKIjElw\nSQghhBBCCCGEEEIIIYQQQmRMgktCCCGEEEIIIYQQQgghhBAiYxJcEkIIIYQQQgghhBBCCCGEEBmT\n4JIQQgghhBBCCCGEEEIIIYTImASXRFZRSt2vlNJD/Lw1yH6GUupzSqmtSimfUqpbKfWCUurfDvV7\nEOJQG027UUptHGafJ8fjvQhxqCml8pRSX1ZKbVFKdSmlAkqp3UqpDUqp1WnKS38jpryRtBvpb8RU\nppRaN8zvf+rP7DT7X2z3Md12n7PV7oPk//li0hptuxnttQQhJhOlVI1S6k6l1NtKqaBSKqSUqlVK\n/VgpNX+I/aS/EVPWSNvNVOtvnONdASFGaTPwbpr1Tf1XKKUcwO+BswAv8DSQA5wKPKiUOl5r/YUx\nrKsQE0XG7SbFU0BzmvU7DkqNhJjAlFLzsPqMhVjt5O9ADJgDnAP8C6tdJcpLfyOmvJG2mxTS34ip\nqBn4xRDbjwOOAOqAfakblFJ3AZ8FQsAzQBSrv/khcKpS6nyttTkWlRZinI263dhG838iIbKeUmoF\n8CxQAjRgffcCWAlcDVyilPqQ1vrFfvtJfyOmrNG2G9uU6G8kuCSy1c+11vdnWPaLWBf6dgKnaK1b\nAJRSi4AXgGuUUs9qrf84JjUVYuIYSbtJ+LbWeuMY1EW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"text/plain": [ "
" ] }, "metadata": { "tags": [], "image/png": { "width": 843, "height": 285 } } } ] }, { "metadata": { "colab_type": "text", "id": "rtcc9pBFIA0X" }, "cell_type": "markdown", "source": [ "The 95% credible interval, or 95% CI, painted in purple, represents the interval, for each temperature, that contains 95% of the distribution. For example, at 65 degrees, we can be 95% sure that the probability of defect lies between 0.25 and 0.85.\n", "\n", "More generally, we can see that as the temperature nears 60 degrees, the CI's spread out over $[0,1]$ quickly. As we pass 70 degrees, the CI's tighten again. This can give us insight about how to proceed next: we should probably test more O-rings around 60-65 temperature to get a better estimate of probabilities in that range. Similarly, when reporting to scientists your estimates, you should be very cautious about simply telling them the expected probability, as we can see this does not reflect how *wide* the posterior distribution is." ] }, { "metadata": { "colab_type": "text", "id": "lesq_3oIIA0Y" }, "cell_type": "markdown", "source": [ "### What about the day of the Challenger disaster?\n", "\n", "On the day of the Challenger disaster, the outside temperature was 31 degrees Fahrenheit. What is the posterior distribution of a defect occurring, given this temperature? The distribution is plotted below. It looks almost guaranteed that the Challenger was going to be subject to defective O-rings." ] }, { "metadata": { "colab_type": "code", "id": "AYbamYmdUdBZ", "outputId": "42a2542e-677f-4786-e39c-fcae90c30559", "colab": { "base_uri": "https://localhost:8080/", "height": 246 } }, "cell_type": "code", "source": [ "plt.figure(figsize(12.5, 3))\n", "\n", "prob_31 = logistic(31, posterior_beta_, posterior_alpha_)\n", "\n", "[ prob_31_ ] = evaluate([ prob_31 ])\n", "\n", "plt.xlim(0.98, 1)\n", "plt.hist(prob_31_, bins=10, density=True, histtype='stepfilled')\n", "plt.title(\"Posterior distribution of probability of defect, given $t = 31$\")\n", "plt.xlabel(\"probability of defect occurring in O-ring\");" ], "execution_count": 57, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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" ] }, "metadata": { "tags": [], "image/png": { "width": 847, "height": 229 } } } ] }, { "metadata": { "colab_type": "text", "id": "WjAFZ8W9IA0c" }, "cell_type": "markdown", "source": [ "### Is our model appropriate?\n", "\n", "The skeptical reader will say \"You deliberately chose the logistic function for $p(t)$ and the specific priors. Perhaps other functions or priors will give different results. How do I know I have chosen a good model?\" This is absolutely true. To consider an extreme situation, what if I had chosen the function $p(t) = 1,\\; \\forall t$, which guarantees a defect always occurring: I would have again predicted disaster on January 28th. Yet this is clearly a poorly chosen model. On the other hand, if I did choose the logistic function for $p(t)$, but specified all my priors to be very tight around 0, likely we would have very different posterior distributions. How do we know our model is an expression of the data? This encourages us to measure the model's **goodness of fit**.\n", "\n", "We can think: *how can we test whether our model is a bad fit?* An idea is to compare observed data with artificial dataset which we can simulate. The rationale is that if the simulated dataset does not appear similar, statistically, to the observed dataset, then likely our model is not accurately represented the observed data. \n", "\n", "Previously in this Chapter, we simulated an artificial dataset for the SMS example. To do this, we sampled values from the priors. We saw how varied the resulting datasets looked like, and rarely did they mimic our observed dataset. In the current example, we should sample from the *posterior* distributions to create *very plausible datasets*. Luckily, our Bayesian framework makes this very easy. We only need to gather samples from the distribution of choice, and specify the number of samples, the shape of the samples (we had 21 observations in our original dataset, so we'll make the shape of each sample 21), and the probability we want to use to determine the ratio of 1 observations to 0 observations.\n", "\n", "\n", "Hence we create the following:\n", "\n", "```python\n", "simulated_data = tfd.Bernoulli(name=\"simulation_data\", probs=p).sample(sample_shape=N)\n", "```\n", "Let's simulate 10 000:" ] }, { "metadata": { "colab_type": "code", "id": "MvFwyz9hwROg", "colab": {} }, "cell_type": "code", "source": [ "alpha = alpha_mean_ # We're basing these values on the outputs of our model above\n", "beta = beta_mean_\n", "p_deterministic = tfd.Deterministic(name=\"p\", loc=1.0/(1. + tf.exp(beta * temperature_ + alpha))).sample()#seed=6.45)\n", "simulated_data = tfd.Bernoulli(name=\"bernoulli_sim\", \n", " probs=p_deterministic_).sample(sample_shape=10000)\n", "[ \n", " bernoulli_sim_samples_,\n", " p_deterministic_\n", "] =evaluate([\n", " simulated_data,\n", " p_deterministic\n", "])" ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "code", "id": "gDyVY1wmgjx4", "outputId": "f033f0d4-7e3b-4371-fe9d-ef2fc8d008d5", "colab": { "base_uri": "https://localhost:8080/", "height": 742 } }, "cell_type": "code", "source": [ "simulations_ = bernoulli_sim_samples_\n", "print(\"Number of simulations: \", simulations_.shape[0])\n", "print(\"Number data points per simulation: \", simulations_.shape[1])\n", "\n", "plt.figure(figsize(12.5, 12))\n", "plt.title(\"Simulated dataset using posterior parameters\")\n", "for i in range(4):\n", " ax = plt.subplot(4, 1, i+1)\n", " plt.scatter(temperature_, simulations_[1000*i, :], color=\"k\",\n", " s=50, alpha=0.6)\n", " " ], "execution_count": 67, "outputs": [ { "output_type": "stream", "text": [ "Number of simulations: 10000\n", "Number data points per simulation: 23\n" ], "name": "stdout" }, { 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" ] }, "metadata": { "tags": [], "image/png": { "width": 827, "height": 689 } } } ] }, { "metadata": { "colab_type": "text", "id": "RFSaMzNQIA0l" }, "cell_type": "markdown", "source": [ "Note that the above plots are different (if you can think of a cleaner way to present this, please send a pull request and answer [here](http://stats.stackexchange.com/questions/53078/how-to-visualize-bayesian-goodness-of-fit-for-logistic-regression)!).\n", "\n", "We wish to assess how good our model is. \"Good\" is a subjective term of course, so results must be relative to other models. \n", "\n", "We will be doing this graphically as well, which may seem like an even less objective method. The alternative is to use *Bayesian p-values*. These are still subjective, as the proper cutoff between good and bad is arbitrary. Gelman emphasises that the graphical tests are more illuminating [3] than p-value tests. We agree.\n", "\n", "The following graphical test is a novel data-viz approach to logistic regression. The plots are called *separation plots*[4]. For a suite of models we wish to compare, each model is plotted on an individual separation plot. I leave most of the technical details about separation plots to the very accessible [original paper](https://onlinelibrary.wiley.com/doi/10.1111/j.1540-5907.2011.00525.x), but I'll summarize their use here.\n", "\n", "For each model, we calculate the proportion of times the posterior simulation proposed a value of 1 for a particular temperature, i.e. compute $P( \\;\\text{Defect} = 1 | t, \\alpha, \\beta )$ by averaging. This gives us the posterior probability of a defect at each data point in our dataset. For example, for the model we used above:" ] }, { "metadata": { "colab_type": "code", "id": "3ho1cPLAIA0l", "outputId": "643b1bf8-6317-48f8-e9c7-74c990e11742", "colab": { "base_uri": "https://localhost:8080/", "height": 449 } }, "cell_type": "code", "source": [ "posterior_probability_ = simulations_.mean(axis=0)\n", "print(\"posterior prob of defect | realized defect \")\n", "for i in range(len(D_)):\n", " print(\"%.2f | %d\" % (posterior_probability_[i], D_[i]))" ], "execution_count": 68, "outputs": [ { "output_type": "stream", "text": [ "posterior prob of defect | realized defect \n", "0.47 | 0\n", "0.20 | 1\n", "0.25 | 0\n", "0.31 | 0\n", "0.39 | 0\n", "0.11 | 0\n", "0.08 | 0\n", "0.19 | 0\n", "0.94 | 1\n", "0.71 | 1\n", "0.19 | 1\n", "0.02 | 0\n", "0.39 | 0\n", "0.99 | 1\n", "0.39 | 0\n", "0.05 | 0\n", "0.19 | 0\n", "0.01 | 0\n", "0.03 | 0\n", "0.01 | 0\n", "0.04 | 1\n", "0.03 | 0\n", "0.92 | 1\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "-q4yysOiIA0n" }, "cell_type": "markdown", "source": [ "Next we sort each column by the posterior probabilities:" ] }, { "metadata": { "colab_type": "code", "id": "i3TkXUhSIA0n", "outputId": "8b269843-6e8c-4757-b712-de7a56364cb4", "colab": { "base_uri": "https://localhost:8080/", "height": 449 } }, "cell_type": "code", "source": [ "ix_ = np.argsort(posterior_probability_)\n", "print(\"probb | defect \")\n", "for i in range(len(D_)):\n", " print(\"%.2f | %d\" % (posterior_probability_[ix_[i]], D_[ix_[i]]))" ], "execution_count": 69, "outputs": [ { "output_type": "stream", "text": [ "probb | defect \n", "0.01 | 0\n", "0.01 | 0\n", "0.02 | 0\n", "0.03 | 0\n", "0.03 | 0\n", "0.04 | 1\n", "0.05 | 0\n", "0.08 | 0\n", "0.11 | 0\n", "0.19 | 0\n", "0.19 | 0\n", "0.19 | 1\n", "0.20 | 1\n", "0.25 | 0\n", "0.31 | 0\n", "0.39 | 0\n", "0.39 | 0\n", "0.39 | 0\n", "0.47 | 0\n", "0.71 | 1\n", "0.92 | 1\n", "0.94 | 1\n", "0.99 | 1\n" ], "name": "stdout" } ] }, { "metadata": { "colab_type": "text", "id": "ajvopQADIA0p" }, "cell_type": "markdown", "source": [ "We can present the above data better in a figure: we've created a `separation_plot` function." ] }, { "metadata": { "colab_type": "code", "id": "tFR1_yu8IA0p", "outputId": "a3d0a1cb-9b41-4f8e-c0d8-ff7b8ef31489", "colab": { "base_uri": "https://localhost:8080/", "height": 236 } }, "cell_type": "code", "source": [ "import matplotlib.pyplot as plt\n", "\n", "def separation_plot( p, y, **kwargs ):\n", " \"\"\"\n", " This function creates a separation plot for logistic and probit classification. \n", " See https://onlinelibrary.wiley.com/doi/10.1111/j.1540-5907.2011.00525.x\n", " \n", " p: The proportions/probabilities, can be a nxM matrix which represents M models.\n", " y: the 0-1 response variables.\n", " \n", " \"\"\" \n", " assert p.shape[0] == y.shape[0], \"p.shape[0] != y.shape[0]\"\n", " n = p.shape[0]\n", "\n", " try:\n", " M = p.shape[1]\n", " except:\n", " p = p.reshape( n, 1 )\n", " M = p.shape[1]\n", "\n", " colors_bmh = np.array( [\"#eeeeee\", \"#348ABD\"] )\n", "\n", "\n", " fig = plt.figure( )\n", " \n", " for i in range(M):\n", " ax = fig.add_subplot(M, 1, i+1)\n", " ix = np.argsort( p[:,i] )\n", " #plot the different bars\n", " bars = ax.bar( np.arange(n), np.ones(n), width=1.,\n", " color = colors_bmh[ y[ix].astype(int) ], \n", " edgecolor = 'none')\n", " ax.plot( np.arange(n+1), np.append(p[ix,i], p[ix,i][-1]), \"k\",\n", " linewidth = 1.,drawstyle=\"steps-post\" )\n", " #create expected value bar.\n", " ax.vlines( [(1-p[ix,i]).sum()], [0], [1] )\n", " plt.xlim( 0, n)\n", " \n", " plt.tight_layout()\n", " \n", " return\n", "\n", "plt.figure(figsize(11., 3))\n", "separation_plot(posterior_probability_, D_)" ], "execution_count": 70, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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" ] }, "metadata": { "tags": [], "image/png": { "width": 777, "height": 201 } } } ] }, { "metadata": { "colab_type": "text", "id": "tBuY2lSaIA0s" }, "cell_type": "markdown", "source": [ "The snaking-line is the sorted probabilities, blue bars denote defects, and empty space (or grey bars for the optimistic readers) denote non-defects. As the probability rises, we see more and more defects occur. On the right hand side, the plot suggests that as the posterior probability is large (line close to 1), then more defects are realized. This is good behaviour. Ideally, all the blue bars *should* be close to the right-hand side, and deviations from this reflect missed predictions. \n", "\n", "The black vertical line is the expected number of defects we should observe, given this model. This allows the user to see how the total number of events predicted by the model compares to the actual number of events in the data.\n", "\n", "It is much more informative to compare this to separation plots for other models. Below we compare our model (top) versus three others:\n", "\n", "1. the perfect model, which predicts the posterior probability to be equal 1 if a defect did occur.\n", "2. a completely random model, which predicts random probabilities regardless of temperature.\n", "3. a constant model: where $P(D = 1 \\; | \\; t) = c, \\;\\; \\forall t$. The best choice for $c$ is the observed frequency of defects, in this case 7/23. \n" ] }, { "metadata": { "colab_type": "code", "id": "RbX1nHrBIA0s", "outputId": "fb96b5c1-3e3d-424e-d9bd-3ba831e7b13b", "colab": { "base_uri": "https://localhost:8080/", "height": 599 } }, "cell_type": "code", "source": [ "plt.figure(figsize(11., 2))\n", "\n", "# Our temperature-dependent model\n", "separation_plot(posterior_probability_, D_)\n", "plt.title(\"Temperature-dependent model\")\n", "\n", "# Perfect model\n", "# i.e. the probability of defect is equal to if a defect occurred or not.\n", "p_ = D_\n", "separation_plot(p_, D_)\n", "plt.title(\"Perfect model\")\n", "\n", "# random predictions\n", "p_ = np.random.rand(23)\n", "separation_plot(p_, D_)\n", "plt.title(\"Random model\")\n", "\n", "# constant model\n", "constant_prob_ = 7./23 * np.ones(23)\n", "separation_plot(constant_prob_, D_)\n", "plt.title(\"Constant-prediction model\");" ], "execution_count": 71, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ] }, "metadata": { "tags": [] } }, { "output_type": "display_data", "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "tags": [], "image/png": { "width": 777, "height": 141 } } } ] }, { "metadata": { "colab_type": "text", "id": "etHuMg8OIA0u" }, "cell_type": "markdown", "source": [ "In the random model, we can see that as the probability increases there is no clustering of defects to the right-hand side. Similarly for the constant model.\n", "\n", "In the perfect model, the probability line is not well shown, as it is stuck to the bottom and top of the figure. Of course the perfect model is only for demonstration, and we cannot infer any scientific inference from it." ] }, { "metadata": { "colab_type": "text", "id": "_I_3h7lsIA0v" }, "cell_type": "markdown", "source": [ "## Exercises\n", "\n", "1\\. Try putting in extreme values for our observations in the cheating example. What happens if we observe 25 affirmative responses? 10? 50? " ] }, { "metadata": { "colab_type": "code", "id": "_B-K0Neyx7pZ", "colab": {} }, "cell_type": "code", "source": [ "#type your code here." ], "execution_count": 0, "outputs": [] }, { "metadata": { "colab_type": "text", "id": "ulECHYwMIA0v" }, "cell_type": "markdown", "source": [ "2\\. Try plotting $\\alpha$ samples versus $\\beta$ samples. Why might the resulting plot look like this?" ] }, { "metadata": { "colab_type": "code", "id": "21v-EuHZIA0v", "outputId": "06301247-795c-4077-bdfc-bd5bb9b345a9", "colab": { "base_uri": "https://localhost:8080/", "height": 259 } }, "cell_type": "code", "source": [ "#type your code here.\n", "plt.figure(figsize(12.5, 4))\n", "\n", "plt.scatter(alpha_samples_, beta_samples_, alpha=0.1)\n", "plt.title(\"Why does the plot look like this?\")\n", "plt.xlabel(r\"$\\alpha$\")\n", "plt.ylabel(r\"$\\beta$\");" ], "execution_count": 73, "outputs": [ { "output_type": "error", "ename": "NameError", "evalue": "ignored", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfigsize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m12.5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscatter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0malpha_samples_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbeta_samples_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0malpha\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtitle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Why does the plot look like this?\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mxlabel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mr\"$\\alpha$\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'alpha_samples_' is not defined" ] }, { "output_type": "display_data", "data": { "text/plain": [ "
" ] }, "metadata": { "tags": [] } } ] }, { "metadata": { "colab_type": "text", "id": "e6RYS1_jIA0y" }, "cell_type": "markdown", "source": [ "## References\n", "\n", "[1] Dalal, Fowlkes and Hoadley (1989),JASA, 84, 945-957.\n", "\n", "[2] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. .\n", "\n", "[3] Gelman, Andrew. \"Philosophy and the practice of Bayesian statistics.\" British Journal of Mathematical and Statistical Psychology. (2012): n. page. Web. 2 Apr. 2013.\n", "\n", "[4] Greenhill, Brian, Michael D. Ward, and Audrey Sacks. \"The Separation Plot: A New Visual Method for Evaluating the Fit of Binary Models.\" American Journal of Political Science. 55.No.4 (2011): n. page. Web. 2 Apr. 2013.\n" ] } ] }