mlegp (version 2.2.6)

FANOVA: Sensitivity Analysis for Gaussian Processes and Gaussian Process Lists

Description

Functional Analysis of Variance (FANOVA) Functions for Gaussian Processes

Usage

OverallMean(gp, lower = apply(gp$X, 2, min), upper = apply(gp$X, 2, max))
FunctionalVariance(gp, lower = apply(gp$X, 2, min), upper = apply(gp$X, 2, max), mu0 = NULL)
ANOVAMainEffect(gp, effectNum, lower = apply(gp$X, 2, min), upper = apply(gp$X, 2, max))
ANOVAInteractionEffect(gp, effectNums, mu0 = NULL, lower = apply(gp$X, 2, min), upper = apply(gp$X, 2, max), 
	maxpts = NULL)

Arguments

gp

an object of type gp

lower

a vector of minimum values for ALL parameters of the gp design matrix

upper

a vector of maximum values for ALL parameters of the gp design matrix

effectNum

the effect number or name of the desired main effect

effectNums

a vector of 2 elements corresponding to the effect numbers or names of the desired interaction effect

mu0

the overall mean, useful for speeding up computations

maxpts

the maximum number of function evaluations used in the calculation of each predicted output, see adapt

Value

• OverallMean returns the mean value of the Gaussian process predictor

  FunctionalVariance returns the overall variance of the Gaussian process predictor

  ANOVAMainEffect returns the variation due to the single effect specified by effectNum

  ANOVAInteractionEffect returns the variation due to the joint two-way effect specified by effectNms

Details

Implements the FANOVA decomposition of Schonlau and Welch (2006), for main and two-way factor effects, using a prior distribution of all components that is ~ independent U(a,b), where (a,b) corresponds to the (min,max) value of that component in the design. For all parameters, (a,b) can be overwritten via the arguments lower and upper.

OverallMean and ANOVAMainEffect use the function integrate for integration; FunctionalVariance and ANOVAInteractionEffect also use the library adapt for multi-dimensional integration.

References

Schonlau, M. and Welch, W. 2006. Screening the Input Variables to a Computer Model Via Analysis of Variance and Visualization, in Screening: Methods for Experimentation in Industry, Drug Discovery, and Genetics. A Dean and S. Lewis, eds. (New York: Springer).

http://users.nsula.edu/dancikg/mlegp/

See Also

The user does not have to directly call these functions, and instead should use FANOVADecomposition

integrate and package adapt for details on single and multi-dimensional integration

Examples

## do not run the following code unless the library adapt is loaded ##
## fit the Gaussian process ##
x1 = kronecker(seq(0,1,by=.25), rep(1,5))
x2 = rep(seq(0,1,by=.25),5)
z = 4 * x1 - 2*x2 + x1 * x2 + rnorm(length(x1))
fit = mlegp(cbind(x1,x2), z, param.names = c("x1", "x2"))

## calculate the proportion of total variance accounted for by x1 ##

ANOVAMainEffect(fit, "x1") / FunctionalVariance(fit) * 100
## check this against 'FANOVADecomposition' ##
FANOVADecomposition(fit)