sensitivity (version 1.30.1)

EPtest: Non-parametric variable significance test based on the empirical process

Description

EPtest builds the non-parametric variable significance test from Klein and Rochet (2022) for the null hypothesis \(H_0: S^u = S\) where \(S^u\) is the Sobol index for the inputs \(X_i, i \in u\) ans \(S\) is the Sobol index for all the inputs in \(X\).

Usage

EPtest(X, y, u = NULL, doe = NULL, Kdoe = 10, tau = 0.1)

Value

EPtest returns a list containing:

statistics

The test statistics that follows a chi-squared distribution under the null hypothesis.

ddl

The number of degrees of freedom used in the limit chi-square distribution for the test.

p-value

The test p-value.

Arguments

X

a matrix or data.frame that contains the numerical inputs as columns.

y

a vector of output.

u

the vector of indices of the columns of X for which we want to test the significance.

doe

the design of experiment on which the empirical process is to be evaluated. It should be independent from X.

Kdoe

if doe is null and Kdoe is specified, the design of experiment is taken as Kdoe points drawn uniformly independently on intervals delimited by the range of each input.

tau

a regularization parameter to approximate the limit chi2 distribution of the test statistics under H0.

Author

Paul Rochet

References

T. Klein and P. Rochet, Test comparison for Sobol Indices over nested sets of variables, SIAM/ASA Journal on Uncertainty Quantification 10.4 (2022): 1586-1600.

See Also

sobol

Examples

# Model: Ishigami
  
n = 100
X = matrix(runif(3*n, -pi, pi), ncol = 3)
  
y = ishigami.fun(X)
	
# Test the significance of X1, H0: S1 = 0
EPtest(X[, 1], y, u = NULL)

# Test if X1 is sufficient to explain Y, H0: S1 = S123
EPtest(X, y, u = 1)
  
# Test if X3 is significant in presence of X2, H0: S2 = S23
EPtest(X[, 2:3], y, u = 1)