```
## the example here illustrates how fcalib combines aGP.seq and
## discrep.est functions, duplicating the example in the discrep.est
## documentation file. It is comprised of snippets from demo("calib"),
## which contains code from the Calibration Section of vignette("laGP")
## Here we generate calibration data using a true calibration
## parameter, u, and then evaluate log posterior probabilities;
## the discrep.est documentation repeats this with by first calling
## aGP.seq and then discrep.est. The answers should be identical, however
## note that a call first to example("fcalib") and then
## example("discrep.est") will generate two random data sets, causing
## the results not to match
## begin data-generation code identical to aGP.seq, discrep.est, fcalib
## example sections and demo("calib")
## M: computer model test function used in Goh et al, 2013 (Technometrics)
## an elaboration of one from Bastos and O'Hagan, 2009 (Technometrics)
M <- function(x,u)
{
x <- as.matrix(x)
u <- as.matrix(u)
out <- (1-exp(-1/(2*x[,2])))
out <- out * (1000*u[,1]*x[,1]^3+1900*x[,1]^2+2092*x[,1]+60)
out <- out / (100*u[,2]*x[,1]^3+500*x[,1]^2+4*x[,1]+20)
return(out)
}
## bias: discrepancy function from Goh et al, 2013
bias <- function(x)
{
x<-as.matrix(x)
out<- 2*(10*x[,1]^2+4*x[,2]^2) / (50*x[,1]*x[,2]+10)
return(out)
}
## beta.prior: marginal beta prior for u,
## defaults to a mode at 1/2 in hypercube
beta.prior <- function(u, a=2, b=2, log=TRUE)
{
if(length(a) == 1) a <- rep(a, length(u))
else if(length(a) != length(u)) stop("length(a) must be 1 or length(u)")
if(length(b) == 1) b <- rep(b, length(u))
else if(length(b) != length(u)) stop("length(b) must be 1 or length(u)")
if(log) return(sum(dbeta(u, a, b, log=TRUE)))
else return(prod(dbeta(u, a, b, log=FALSE)))
}
## tgp for LHS sampling
library(tgp)
rect <- matrix(rep(0:1, 4), ncol=2, byrow=2)
## training inputs
ny <- 50;
X <- lhs(ny, rect[1:2,]) ## computer model train
## true (but unknown) setting of the calibration parameter
## for the computer model
u <- c(0.2, 0.1)
Zu <- M(X, matrix(u, nrow=1))
## field data response, biased and replicated
sd <- 0.5
## Y <- computer output + bias + noise
reps <- 2 ## example from paper uses reps <- 10
Y <- rep(Zu,reps) + rep(bias(X),reps) + rnorm(reps*length(Zu), sd=sd)
## variations: remove the bias or change 2 to 1 to remove replicates
## computer model design
nz <- 10000
XU <- lhs(nz, rect)
nth <- 1 ## number of threads to use in emulation, demo uses 8
## augment with physical model design points
## with various u settings
XU2 <- matrix(NA, nrow=10*ny, ncol=4)
for(i in 1:10) {
I <- ((i-1)*ny+1):(ny*i)
XU2[I,1:2] <- X
}
XU2[,3:4] <- lhs(10*ny, rect[3:4,])
XU <- rbind(XU, XU2)
## evaluate the computer model
Z <- M(XU[,1:2], XU[,3:4])
## flag indicating if estimating bias/discrepancy or not
bias.est <- TRUE
## two passes of ALC with MLE calculations for aGP.seq
methods <- rep("alcray", 2) ## demo uses rep("alc", 2)
## set up priors
da <- d <- darg(NULL, XU)
g <- garg(list(mle=TRUE), Y)
## end identical data generation code
## now calculate log posterior for true calibration parameter
## value (u). You could repeat this for an estimate value
## from demo("calib"), for example u.hat <- c(0.8236673, 0.1406989)
fcalib(u, XU, Z, X, Y, da, d, g, beta.prior, methods, M, bias.est, nth)
```

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