Log-Odds Bayesian Update

Problem

In log-odds form, Bayes' rule becomes additive: log posterior odds = log prior odds + sum of the log likelihood ratios. Given the log prior odds and a list of log likelihood ratios, return the log posterior odds. An empty list leaves the prior odds unchanged.

Hint

Multiplying odds by likelihood ratios becomes adding their logarithms.

Test cases

case 1

in: [0,[1]]

expected: 1

case 2

in: [0,[]]

expected: 0

case 3

in: [-2,[0.5,0.5]]

expected: -1

case 4

in: [1.5,[-0.5,2,-1]]

expected: 2

case 5

in: [-1,[0.25,-0.75]]

expected: -1.5

Starter codePython

def log_odds_bayesian_update(log_prior_odds, log_likelihood_ratios):
    # Your code here
    pass

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