Gaussian Gibbs Conditional Mean

Problem

For a bivariate Gaussian with means mu1 and mu2, standard deviations sigma1 and sigma2, and correlation rho, the conditional mean of the first coordinate given the second is mu1 + rho * (sigma1 / sigma2) * (x2 - mu2). Return that mean, or 0.0 for invalid parameters.

Hint

This is the Gibbs sampling update for one coordinate of a bivariate normal.

Test cases

case 1

in: [0,0,1,1,0.5,1]

expected: 0.5

case 2

in: [1,2,2,1,0.5,3]

expected: 2

case 3

in: [0,0,1,2,0.8,4]

expected: 1.6

case 4

in: [3,3,1,1,0,7]

expected: 3

case 5

in: [0,0,1,1,1.5,1]

expected: 0

Starter codePython

def gaussian_gibbs_conditional_mean(mu1, mu2, sigma1, sigma2, rho, x2):
    # Your code here
    pass

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