Markov-Switching Smoothed Probability

Problem

Update regime probabilities with one observation. Starting from filtered_probs, propagate through the transition matrix, multiply elementwise by the emission likelihoods, and normalize to sum to 1.

Return the updated probability vector; when the total is zero return the filtered probabilities unchanged.

Hint

The transition step spreads probability before the observation reweights the states.

Test cases

case 1

in: [[0.6,0.4],[[0.9,0.1],[0.2,0.8]],[0.7,0.3]]

expected: [0.7919708029197081,0.208029197080292]

case 2

in: [[1,0],[[0.9,0.1],[0.2,0.8]],[0.5,0.5]]

expected: [0.9,0.1]

case 3

in: [[0.5,0.5],[[0.5,0.5],[0.5,0.5]],[1,1]]

expected: [0.5,0.5]

case 4

in: [[0,0],[[0.5,0.5],[0.5,0.5]],[1,1]]

expected: [0,0]

Starter codePython

def markov_switching_smoothed_probability(filtered_probs, transition_matrix, emission_probs):
    # Your code here
    pass

4 test cases · run your code against them in the editor