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) # }