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Author: Harald Schilly
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Pymc3: Probabilistic Programming in Python: Bayesian Modeling and Probabilistic Machine Learning

Available in the "Python 3 (Ubuntu Linux)" kernel.

http://docs.pymc.io/intro.html

In [1]:
import pymc3 as pm pm.__version__
/usr/local/lib/python3.5/dist-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`. from ._conv import register_converters as _register_converters
'3.3'
In [2]:
import numpy as np import matplotlib.pyplot as plt # Initialize random number generator np.random.seed(123) # True parameter values alpha, sigma = 1, 1 beta = [1, 2.5] # Size of dataset size = 100 # Predictor variable X1 = np.random.randn(size) X2 = np.random.randn(size) * 0.2 # Simulate outcome variable Y = alpha + beta[0]*X1 + beta[1]*X2 + np.random.randn(size)*sigma
In [3]:
basic_model = pm.Model() with basic_model: # Priors for unknown model parameters alpha = pm.Normal('alpha', mu=0, sd=10) beta = pm.Normal('beta', mu=0, sd=10, shape=2) sigma = pm.HalfNormal('sigma', sd=1) # Expected value of outcome mu = alpha + beta[0]*X1 + beta[1]*X2 # Likelihood (sampling distribution) of observations Y_obs = pm.Normal('Y_obs', mu=mu, sd=sigma, observed=Y)
In [4]:
map_estimate = pm.find_MAP(model=basic_model) map_estimate
0%| | 0/5000 [00:00<?, ?it/s] logp = -328.33, ||grad|| = 464.32: 0%| | 0/5000 [00:00<?, ?it/s] logp = -149.58, ||grad|| = 12.242: 0%| | 10/5000 [00:00<00:08, 600.73it/s] logp = -149.58, ||grad|| = 12.242: 100%|██████████| 19/19 [00:00<00:00, 792.13it/s]
{'alpha': array(0.90660093), 'beta': array([0.94848596, 2.60711845]), 'sigma': array(0.96298858), 'sigma_log__': array(-0.03771373)}
In [5]:
with basic_model: # draw 500 posterior samples trace = pm.sample()
Auto-assigning NUTS sampler... Initializing NUTS using jitter+adapt_diag... Sequential sampling (2 chains in 1 job) NUTS: [sigma_log__, beta, alpha] 0%| | 0/1000 [00:00<?, ?it/s] 2%|▏ | 20/1000 [00:00<00:04, 197.94it/s] 6%|▌ | 56/1000 [00:00<00:03, 277.97it/s] 10%|█ | 105/1000 [00:00<00:02, 347.37it/s] 17%|█▋ | 167/1000 [00:00<00:02, 414.59it/s] 21%|██▏ | 214/1000 [00:00<00:01, 418.35it/s] 26%|██▌ | 262/1000 [00:00<00:01, 427.73it/s] 32%|███▏ | 320/1000 [00:00<00:01, 448.36it/s] 39%|███▊ | 387/1000 [00:00<00:01, 475.04it/s] 45%|████▌ | 452/1000 [00:00<00:01, 493.81it/s] 53%|█████▎ | 527/1000 [00:01<00:00, 518.26it/s] 60%|██████ | 600/1000 [00:01<00:00, 536.98it/s] 68%|██████▊ | 685/1000 [00:01<00:00, 562.65it/s] 77%|███████▋ | 773/1000 [00:01<00:00, 586.03it/s] 86%|████████▋ | 864/1000 [00:01<00:00, 608.69it/s] 95%|█████████▍| 948/1000 [00:01<00:00, 623.57it/s] 100%|██████████| 1000/1000 [00:01<00:00, 630.44it/s] 0%| | 0/1000 [00:00<?, ?it/s] 6%|▌ | 61/1000 [00:00<00:01, 602.42it/s] 12%|█▏ | 116/1000 [00:00<00:01, 571.29it/s] 18%|█▊ | 177/1000 [00:00<00:01, 582.86it/s] 24%|██▍ | 242/1000 [00:00<00:01, 593.95it/s] 30%|███ | 305/1000 [00:00<00:01, 599.09it/s] 37%|███▋ | 374/1000 [00:00<00:01, 613.40it/s] 44%|████▍ | 439/1000 [00:00<00:00, 617.81it/s] 50%|████▉ | 499/1000 [00:00<00:00, 615.04it/s] 56%|█████▌ | 560/1000 [00:00<00:00, 613.53it/s] 62%|██████▏ | 620/1000 [00:01<00:00, 603.46it/s] 69%|██████▊ | 687/1000 [00:01<00:00, 609.12it/s] 75%|███████▌ | 753/1000 [00:01<00:00, 612.96it/s] 82%|████████▏ | 815/1000 [00:01<00:00, 609.45it/s] 88%|████████▊ | 876/1000 [00:01<00:00, 601.87it/s] 93%|█████████▎| 934/1000 [00:01<00:00, 594.19it/s] 99%|█████████▉| 990/1000 [00:01<00:00, 585.46it/s] 100%|██████████| 1000/1000 [00:01<00:00, 581.02it/s]
In [6]:
trace['alpha'][-5:]
array([0.9572314 , 0.93554263, 0.86782858, 0.97563444, 0.70462067])
In [7]:
_ = pm.traceplot(trace)
In [8]:
pm.summary(trace)
mean sd mc_error hpd_2.5 hpd_97.5 n_eff Rhat
alpha 0.904619 0.097804 0.002686 0.720830 1.092549 1000.0 0.999163
beta__0 0.947115 0.092629 0.002394 0.744485 1.128060 1000.0 1.001146
beta__1 2.608587 0.538713 0.016015 1.602050 3.685764 1000.0 0.999511
sigma 0.989664 0.072976 0.001916 0.857547 1.140489 1000.0 0.999216
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