Bayesian Shrinkage Rate

Problem

Return the Gamma-Poisson posterior mean rate (events + prior_strength*prior_mean)/(person_time + prior_strength), which shrinks the raw rate toward the prior. Return 0.0 when the denominator is not positive or an input is negative.

Hint

prior_strength acts like extra person-time borrowed from the prior.

Test cases

case 1

in: [10,100,0.05,200]

expected: 0.06666666666666667

case 2

in: [0,100,0.1,100]

expected: 0.05

case 3

in: [50,100,0.02,100]

expected: 0.26

case 4

in: [10,100,0.05,0]

expected: 0.1

case 5

in: [0,0,0.1,0]

expected: 0

Starter codePython

def bayesian_shrinkage_rate(events, person_time, prior_mean, prior_strength):
    # Your code here
    pass

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