log_approx_ref_prior: The natural logarithm of the jointly robust prior (up to a normalizing constant)

Description

A function to the natural logarithm of the jointly robust prior (up to a normalizing constant).

Usage

log_approx_ref_prior(param, nugget, nugget_est, CL, a, b)

Value

The numerical value of the derivative of the approximate reference prior with regard to inverse-range parameters and the nugget-variance ratio parameter. When the nugget is fixed, the derivative is on inverse-range parameters.

Arguments

param: A vector of natural logarithm of inverse-range parameters and natural logarithm of the nugget-variance ratio parameter.
nugget: The nugget-variance ratio parameter if this parameter is fixed.
nugget_est: Boolean value of whether the nugget is estimated or fixed.
CL: Prior parameter in the jointly robust prior.
a: Prior parameter in the jointly robust prior.
b: Prior parameter in the jointly robust prior.

Author

tools:::Rd_package_author("RobustGaSP")

Maintainer: tools:::Rd_package_maintainer("RobustGaSP")

References

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

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

Examples

Run this code

# inputs
x<-runif(10);
n<-length(x);

# default prior parameters
a<-0.2
b<-n^{-1}*(a+1)
R0<-as.matrix(abs(outer(x,x, "-")))
CL<- mean(R0[which(R0>0)])

# compute the density of log reference prior up to a normalizing constant
param <- seq(-10,10,0.01)
prior <- rep(0,length(param))
for(i in 1:length(param)){
  prior[i] <- exp(log_approx_ref_prior(param[i],nugget=0,nugget_est=FALSE,CL,a,b) )
}
# plot
plot(param,prior,type='l',
                xlab='Logarithm of inverse range parameters',
                ylab='Prior density up to a normalizing constant')

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