Gaussian Product of Experts

Problem

A product of independent Gaussian experts with means means[i] and standard deviations sigmas[i] is again Gaussian. Its precision is the sum of the expert precisions 1 / sigmas[i]^2, and its mean is the precision-weighted average of the expert means. Return [mean, standard deviation] or [0.0, 0.0] for empty, mismatched or nonpositive input.

Hint

Multiply the Gaussian densities: precisions add and precision-weighted means add.

Test cases

case 1

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

expected: [0.5,0.7071067811865475]

case 2

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

expected: [0,0.8944271909999159]

case 3

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

expected: [2,0.5773502691896258]

case 4

in: [[2],[0.5]]

expected: [2,0.5]

case 5

in: [[0,10],[1,0.1]]

expected: [9.900990099009901,0.09950371902099892]

Starter codePython

import math


def gaussian_product_of_experts(means, sigmas):
    # Your code here
    pass

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