MOFAT (version 1.0)

measure: Screening measures

Description

This function can be used for computing screening measures.

Usage

measure(design, y)

Value

t

Total Sobol' index

mustar

\(\mu^*\) measure

Arguments

design

design matrix, which should have the Sobol' design structure

y

response vector

Author

Qian Xiao and V. Roshan Joseph

Details

The measure function computes the screening measures such as the total Sobol' indices (Sobol' 1993) and \(\mu^*\) measure of Campolongo et al. (2007). The design matrix should have the Sobol' design structure. Please see Xiao et al. (2022) for details.

References

Sobol’, I. M. (1993), “On sensitivity estimation for nonlinear mathematical models,” Mathematical Modeling and Computational Experiments, 1, 407–414.

Campolongo, F., Cariboni, J., and Saltelli, A. (2007), “An effective screening design for sensitivity analysis of large models,” Environmental modelling and software, 22, 1509–1518.

Xiao, Q., Joseph, V. R., and Ray, D. M. (2022). “Maximum One-Factor-At-A-Time Designs for Screening in Computer Experiments”. Technometrics, to appear.

Examples

#Friedman function
fun <- function (X)
{
 Y <- 10*sin(pi*X[1]*X[2]) + 20*(X[3] - 0.5)^2 + 10*X[4] + 5*X[5]
 return(Y)
}
design = mofat(p=10, l=3)
y = apply(design, 1, fun)

#Screening measures
measure(design, y)