Dirichlet-Multinomial Posterior

Problem

A Dirichlet(alphas) prior over category probabilities is updated with observed category counts. The conjugate posterior keeps the same form with parameters alphas[i] + counts[i]. Return the updated concentration vector, or an empty list when the lengths differ, any alpha is nonpositive, or any count is negative.

Hint

The posterior concentration is the prior concentration plus the observed counts.

Test cases

case 1

in: [[1,2,3],[4,5,6]]

expected: [5,7,9]

case 2

in: [[0.5,0.5],[3,1]]

expected: [3.5,1.5]

case 3

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

expected: [1,1]

case 4

in: [[1,2],[3]]

expected: []

case 5

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

expected: []

Starter codePython

def dirichlet_multinomial_posterior(alphas, counts):
    # Your code here
    pass

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