RobustGaSP-package {RobustGaSP}

Robust Gaussian Stochastic Process Emulation

Description

Robust parameter estimation and prediction of Gaussian stochastic process emulators. It allows for robust parameter estimation and prediction using Gaussian stochastic process emulator. It also implements the parallel partial Gaussian stochastic process emulator for computer model with massive outputs See the reference: Mengyang Gu and Jim Berger, 2016, Annals of Applied Statistics; Mengyang Gu, Xiaojing Wang and Jim Berger, 2018, Annals of Statistics.

Details

The DESCRIPTION file:

Package:	RobustGaSP
Type:	Package
Title:	Robust Gaussian Stochastic Process Emulation
Version:	0.6.6
Date/Publication:	2024-01-14 08:10:03 UTC
Authors@R:	c(person(given="Mengyang",family="Gu",role=c("aut","cre"), email="[e-mail]"), person(given="Jesus",family="Palomo", role=c("aut"), email="[e-mail]"), person(given="James",family="Berger", role="aut"))
Maintainer:	Mengyang Gu <[e-mail]>
Author:	Mengyang Gu [aut, cre], Jesus Palomo [aut], James Berger [aut]
Description:	Robust parameter estimation and prediction of Gaussian stochastic process emulators. It allows for robust parameter estimation and prediction using Gaussian stochastic process emulator. It also implements the parallel partial Gaussian stochastic process emulator for computer model with massive outputs See the reference: Mengyang Gu and Jim Berger, 2016, Annals of Applied Statistics; Mengyang Gu, Xiaojing Wang and Jim Berger, 2018, Annals of Statistics.
License:	GPL-2 | GPL-3
LazyData:	true
Depends:	R (>= 3.5.0), methods
Imports:	Rcpp (>= 0.12.3), nloptr (>= 1.0.4)
LinkingTo:	Rcpp, RcppEigen
NeedsCompilation:	yes
Repository:	CRAN
Packaged:	2019-06-05 02:09:17 UTC; gumengyang
RoxygenNote:	5.0.1

Index of help topics:

RobustGaSP-package      Robust Gaussian Stochastic Process Emulation
findInertInputs         find inert inputs with the posterior mode
humanity.X              data from the humanity model
leave_one_out_rgasp     leave-one-out fitted values and standard
                        deviation for robust GaSP model
plot                    Plot for Robust GaSP model
ppgasp                  Setting up the parallel partial GaSP model
ppgasp-class            PP GaSP class
predict.ppgasp          Prediction for PP GaSP model
predict.rgasp           Prediction for Robust GaSP model
predppgasp-class        Predicted PP GaSP class
predrgasp-class         Predictive robust GaSP class
rgasp                   Setting up the robust GaSP model
rgasp-class             Robust GaSP class
show                    Show Robust GaSP object
show.ppgasp             Show parllel partial Gaussian stochastic
                        process (PP GaSP) object
simulate                Sample for Robust GaSP model

Author(s)

Mengyang Gu [aut, cre], Jesus Palomo [aut], James Berger [aut]

Maintainer: Mengyang Gu <[e-mail]>

References

J.O. Berger, V. De Oliveira and B. Sanso (2001), Objective Bayesian analysis of spatially correlated data, Journal of the American Statistical Association, 96, 1361-1374.

M. Gu. and J.O. Berger (2016). Parallel partial Gaussian process emulation for computer models with massive output. Annals of Applied Statistics, 10(3), 1317-1347.

M. Gu. (2016). Robust uncertainty quantification and scalable computation for computer models with massive output. Ph.D. thesis. Duke University.

M. Gu, X. Wang and J.O. Berger (2018), Robust Gaussian stochastic process emulation, Annals of Statistics, 46(6A), 3038-3066.

M. Gu (2018), Jointly robust prior for Gaussian stochastic process in emulation, calibration and variable selection, arXiv:1804.09329.

R. Paulo (2005), Default priors for Gaussian processes, Annals of statistics, 33(2), 556-582.

J. Sacks, W.J. Welch, T.J. Mitchell, and H.P. Wynn (1989), Design and analysis of computer experiments, Statistical Science, 4, 409-435.

Examples

  #------------------------
  # a 3 dimensional example
  #------------------------
  # dimensional of the inputs
  dim_inputs <- 3    
  # number of the inputs
  num_obs <- 30       
  # uniform samples of design
  input <- matrix(runif(num_obs*dim_inputs), num_obs,dim_inputs) 
  
  # Following codes use maximin Latin Hypercube Design, which is typically better than uniform
  # library(lhs)
  # input <- maximinLHS(n=num_obs, k=dim_inputs)  ##maximin lhd sample
  
  ####
  # outputs from the 3 dim dettepepel.3.data function
  
  output = matrix(0,num_obs,1)
  for(i in 1:num_obs){
    output[i]<-dettepepel.3.data(input[i,])
  }
  
  # use constant mean basis, with no constraint on optimization
  m1<- rgasp(design = input, response = output, lower_bound=FALSE)
  
  # the following use constraints on optimization
  # m1<- rgasp(design = input, response = output, lower_bound=TRUE)
  
  # the following use a single start on optimization
  # m1<- rgasp(design = input, response = output, lower_bound=FALSE)
  
  # number of points to be predicted 
  num_testing_input <- 5000    
  # generate points to be predicted
  testing_input <- matrix(runif(num_testing_input*dim_inputs),num_testing_input,dim_inputs)
  # Perform prediction
  m1.predict<-predict(m1, testing_input, outasS3 = FALSE)
  # Predictive mean
  #m1.predict@mean  
  
  # The following tests how good the prediction is 
  testing_output <- matrix(0,num_testing_input,1)
  for(i in 1:num_testing_input){
    testing_output[i]<-dettepepel.3.data(testing_input[i,])
  }
  
  # compute the MSE, average coverage and average length
  # out of sample MSE
  MSE_emulator <- sum((m1.predict@mean-testing_output)^2)/(num_testing_input)  
  
  # proportion covered by 95% posterior predictive credible interval
  prop_emulator <- length(which((m1.predict@lower95<=testing_output)
                   &(m1.predict@upper95>=testing_output)))/num_testing_input
  
  # average length of  posterior predictive credible interval
  length_emulator <- sum([e-mail]@lower95)/num_testing_input
  
  # output of prediction
  MSE_emulator
  prop_emulator
  length_emulator  
  # normalized RMSE
  sqrt(MSE_emulator/mean((testing_output-mean(output))^2 ))