Empirical Bayes Mean

Problem

Return the empirical Bayes shrunk mean grand + (tau2/(tau2 + within_var/n))*(group_mean - grand), where tau2 is the between-group variance. Return 0.0 when n <= 0, a variance is negative, or the denominator is zero.

Hint

Groups with less data are pulled further toward the grand mean.

Test cases

case 1

in: [12,10,4,1,10]

expected: 11.428571428571429

case 2

in: [12,10,4,1,1]

expected: 10.4

case 3

in: [8,10,4,1,10]

expected: 8.571428571428571

case 4

in: [10,10,1,1,5]

expected: 10

case 5

in: [12,10,4,0,10]

expected: 10

Starter codePython

def empirical_bayes_mean(group_mean, grand_mean, within_var, between_var, n):
    # Your code here
    pass

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