RobustGaSP-package: Robust Gaussian Stochastic Process Emulation

In RobustGaSP: Robust Gaussian Stochastic Process Emulation

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

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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 ))

RobustGaSP documentation built on May 29, 2024, 1:26 a.m.