Bayesian Updating Normal-Normal

Problem

Update a normal prior with n normal observations of known variance: posterior precision = 1/prior_var + n/data_var and posterior mean = post_var * (prior_mean/prior_var + n * xbar/data_var).

Return [posterior_mean, posterior_variance]; return the prior unchanged for empty data or non-positive variances.

Hint

Precisions add: prior precision plus one data precision per observation.

Test cases

case 1

in: [0,1,[1,2,3],1]

expected: [1.5,0.25]

case 2

in: [10,4,[12],2]

expected: [11.333333333333332,1.3333333333333333]

case 3

in: [5,1,[],2]

expected: [5,1]

case 4

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

expected: [0.6666666666666666,0.3333333333333333]

Starter codePython

def bayesian_normal_update(prior_mean, prior_var, data, data_var):
    # Your code here
    pass

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