Fisher Information (Gaussian)

Problem

Return the 2x2 Fisher information matrix for a Gaussian with unknown mean and variance:

diag(1 / var, 1 / (2 * var^2))

The matrix is diagonal and each entry measures how sharply the likelihood responds to one parameter.

Hint

The mean and variance parameters are orthogonal for a Gaussian.

case 1

in: [1]

expected: [[1,0],[0,0.5]]

case 2

in: [2]

expected: [[0.5,0],[0,0.125]]

case 3

in: [0.5]

expected: [[2,0],[0,2]]

case 4

in: [4]

expected: [[0.25,0],[0,0.03125]]

Starter codePython

def fisher_information_gaussian(var):
    # Your code here
    pass

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