805.sagews

hmm.DiscreteHiddenMarkovModel?

transitions=[[0.3, 0.6, 0.1],[0.5,0.2,0.3],[0.4,0.1,0.5]]
emissions=[[0.5, 0.5],[1/3,2/3],[0.75,0.25]]
initial_probabilities=[1/3,1/3,1/3]
observations=['r','b']

model=hmm.DiscreteHiddenMarkovModel(transitions, emissions, initial_probabilities,observations)

model

Discrete Hidden Markov Model with 3 States and 2 Emissions Transition matrix: [0.3 0.6 0.1] [0.5 0.2 0.3] [0.4 0.1 0.5] Emission matrix: [ 0.5 0.5] [0.333333333333 0.666666666667] [ 0.75 0.25] Initial probabilities: [0.33333333333333331, 0.33333333333333331, 0.33333333333333331] Emission symbols: ['r', 'b']

model.log_likelihood(['r','b','r'])

-2.0918484368004622

e^model.log_likelihood(['r','b','r'])

0.123458719135802

states,prob=model.viterbi(['r','b','r'])

states

[0, 1, 0]

e^prob

0.0166666666666667