Beta-Binomial Posterior Predictive Variance

Problem

For a beta-binomial with n future trials after integrating over a Beta(alpha, beta) success probability, the predictive variance is n * p * (1 - p) * (alpha + beta + n) / (alpha + beta + 1), where p = alpha / (alpha + beta). Return 0.0 when alpha or beta is nonpositive or n is negative.

Hint

The predictive variance overdispenses the binomial variance by the factor (alpha + beta + n) / (alpha + beta + 1).

Test cases

case 1

in: [1,1,10]

expected: 10

case 2

in: [2,3,5]

expected: 2

case 3

in: [2,2,1]

expected: 0.25

case 4

in: [3,1,0]

expected: 0

case 5

in: [1,1,2]

expected: 0.6666666666666666

Starter codePython

def beta_binomial_predictive_variance(alpha, beta, n):
    # Your code here
    pass

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