EPtest | R Documentation |
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
.
EPtest(X, y, u = NULL, doe = NULL, Kdoe = 10, tau = 0.1)
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. |
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. |
Paul Rochet
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.
sobol
# 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)
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