eval_GASP_RFP {LinkedGASP}

Evaluation of parameters of a Gaussian stochastic process emulator of a computer model.

Description

This function evaluates parameters of a Gaussian stochastic process emulator of a computer model based on a few observations which are available from the simulator of a computer model.

Usage

eval_GASP_RFP(data, basis, corr.cols, nugget)

Arguments

data

list which consists of three objects: training input values (which may be multivariate, along several dimensions), corresponding output values of a simulator (scalar) and a vector of smoothness parameter(s) along each input direction.

basis

A set of functions in the mean of a Gaussian process. Typically assumed to be linear in one or several dimensions.

corr.cols

specifies which input directions must be included in the specification of a correlation function.

nugget

Parameter which accounts for possible small stochastisity in the output of a computer model. Default is FALSE.

Details

See examples which illustrate inputs specification to the function.

Value

Function returns a list of objects, including estimates of parameters, which is subsequently may be used for construction of a GASP approximation with the estimated parameters and the data involved.

delta

Estimates of range parameters in the correlation function.

eta

Estimates of a nugget.

sigma.sq

Estimates of variance.

data

Input parameter returned for convenience.

nugget

Input parameter returned for convenience.

basis

Input parameter returned for convenience.

corr.cols

Input parameter returned for convenience.

Author(s)

Ksenia N. Kyzyurova, kseniak.ucoz.net.

References

Ksenia N. Kyzyurova, James O. Berger, and Robert L. Wolpert. Coupling computer models through linking their statistical emulators. SIAM/ASA Journal on Uncertainty Quantification, 6(3): 1151-1171, 2018

Gu, M., Wang, X., Berger, J. O. et al. (2018) Robust Gaussian stochastic process emulation. The Annals of Statistics, 46, 3038-3066.

Examples

## Function f1 is a simulator
f1<-function(x){sin(pi*x)}

## One-dimensional inputs are x1
x1 <- seq(-1,1,.37)

## data.f1 contains the list of data inputs (training) and outputs (fD) together with the assumed
## fixed smoothness of a computer model output. This corresponds to the smoothness in a product 
## power exponential correlation function used for construction of the emulator.
data.f1 <- list(training = x1,fD = f1(x1), smooth = 1.99)

## Evaluation of GASP parameters
f1_MLEs = eval_GASP_RFP(data.f1,list(function(x){x^0},function(x){x^1}),1,FALSE)