dopt.gp
Sequential D-Optimal Design for a Stationary Gaussian Process
Create sequential D-Optimal design for a stationary Gaussian process model of fixed parameterization by subsampling from a list of candidates
Usage
dopt.gp(nn, X=NULL, Xcand, iter=5000, verb=0)Arguments
- nn
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)- X
data.frame,matrixor vector of input locations which are forced into (already in) the design- Xcand
data.frame,matrixor vector of candidates from which new design points are subsampled. Must have the same dimension asX, i.e.,ncol(X) == ncol(Xcand)- iter
number of iterations of stochastic accent algorithm, default
5000- verb
positive integer indicating after how many rounds of stochastic approximation to print each progress statement; default
verb=0results in no printing
Details
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
Value
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,]
Note
Inputs X, Xcand containing NaN, NA, Inf are discarded with non-fatal
warnings. If nn > dim(Xcand)[1] then a non-fatal warning is displayed
and execution commences with nn = dim(Xcand)[1]
In the current version there is no progress indicator. You will have to be patient. Creating D-optimal designs is no speedy task
References
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).
See Also
Examples
# 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)
# }