MediumProbabilitypr-072

Dirichlet-Multinomial Probability

Problem

Dirichlet-multinomial probability of a count vector given Dirichlet concentration parameters alphas:

P(counts) = n! / prod(c_i!) * Gamma(A) / Gamma(A + n) * prod(Gamma(a_i + c_i) / Gamma(a_i))

where A = sum(alphas) and n = sum(counts). Return 0.0 for negative counts or nonpositive alphas.

Hint

Combine the multinomial coefficient with the Dirichlet Beta-ratio term.

case 1

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

expected: 0.3333333333333332

case 2

in: [[2,0],[1,1]]

expected: 0.3333333333333332

case 3

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

expected: 0.09999999999999994

case 4

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

expected: 0.2571428571428569

Starter codePython

import math


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

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