Sobol First-Order Index

Problem

First-order Sobol sensitivity index from conditional means, conditional variances and probabilities of a conditioning variable:

S = Var(E[Y | X]) / (E[Var(Y | X)] + Var(E[Y | X])).

Return 0.0 when the total variance is 0 or the inputs are empty.

Hint

Use the law of total variance decomposition and take the fraction explained by the conditioning variable.

case 1

in: [[0,10],[1,1],[0.5,0.5]]

expected: 0.9615384615384616

case 2

in: [[2,4],[3,5],[0.25,0.75]]

expected: 0.14285714285714285

case 3

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

expected: 0

case 4

in: [[],[],[]]

expected: 0

Starter codePython

def sobol_first_order_index(cond_means, cond_vars, probs):
    # Your code here
    pass

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