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)`

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`

, `matrix`

or vector of input locations
which are forced into (already in) the design

Xcand

`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)`

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=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) # }