Sequential Bayesian Update from Likelihoods

Problem

Given prior probabilities over hypotheses and a sequence of observation likelihood vectors, apply Bayes' rule once per observation. Each row likelihood_vectors[t] gives the probability of observation t under every hypothesis, and the posterior after each step becomes the prior for the next. Return the normalized final posterior, or a list of zeros when it has no mass; rows whose length does not match are skipped.

Hint

Multiply the current posterior by each likelihood row, then renormalize.

Test cases

case 1

in: [[0.5,0.5],[[0.9,0.3],[0.8,0.4]]]

expected: [0.8571428571428572,0.14285714285714285]

case 2

in: [[0.2,0.8],[]]

expected: [0.2,0.8]

case 3

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

expected: [1,0]

case 4

in: [[0.3,0.7],[[0,0],[1,1]]]

expected: [0,0]

case 5

in: [[0.25,0.25,0.5],[[2,1,1]]]

expected: [0.4,0.2,0.4]

Starter codePython

def sequential_bayesian_update(priors, likelihood_vectors):
    # Your code here
    pass

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