Create sequential D-Optimal design for a stationary Gaussian process model of fixed parameterization by subsampling from a list of candidates
dopt.gp(nn, X=NULL, Xcand, iter=5000, verb=0)Number of new points in the design. Must
be less than or equal to the number of candidates contained in
Xcand, i.e., nn <= nrow(Xcand)
data.frame, matrix or vector of input locations
which are forced into (already in) the design
data.frame, matrix or vector of candidates
from which new design points are subsampled. Must have the same
dimension as X, i.e.,
ncol(X) == ncol(Xcand)
number of iterations of stochastic accent algorithm,
default 5000
positive integer indicating after how many rounds of
stochastic approximation to print each progress statement;
default verb=0 results in no printing
The output is a list which contains the inputs to, and outputs of, the C code
used to find the optimal design. The chosen design locations can be
accessed as list members XX or equivalently Xcand[fi,].
Input argument: data.frame of inputs X, can be NULL
Input argument: number new points in the design
Input argument: data.frame of candidate locations Xcand
Number of rows in Xcand, i.e., nncand = dim(Xcand)[1]
Vector of length nn describing the selected new design locations
as indices into Xcand
data.frame of selected new design locations, i.e.,
XX = Xcand[fi,]
Design is based on a stationary Gaussian process model with stationary isotropic
exponential correlation function with parameterization fixed as a function
of the dimension of the inputs. The algorithm implemented is a simple stochastic
ascent which maximizes det(K)-- the covariance matrix constructed
with locations X and a subset of Xcand of size nn.
The selected design is locally optimal
Gramacy, R. B. (2020) Surrogates: Gaussian Process Modeling, Design and Optimization for the Applied Sciences. Boca Raton, Florida: Chapman Hall/CRC. (See Chapter 6.) https://bobby.gramacy.com/surrogates/
Chaloner, K. and Verdinelli, I. (1995). Bayesian experimental design: A review. Statist. Sci., 10, (pp. 273--304).
# NOT RUN {
#
# 2-d Exponential data
# (This example is based on random data.
# It might be fun to run it a few times)
#
# get the data
exp2d.data <- exp2d.rand()
X <- exp2d.data$X; Z <- exp2d.data$Z
Xcand <- exp2d.data$XX
# find a treed sequential D-Optimal design
# with 10 more points
dgp <- dopt.gp(10, X, Xcand)
# plot the d-optimally chosen locations
# Contrast with locations chosen via
# the tgp.design function
plot(X, pch=19, xlim=c(-2,6), ylim=c(-2,6))
points(dgp$XX)
# }