tgp (version 2.4-23)

dopt.gp: Sequential D-Optimal Design for a Stationary Gaussian Process

Description

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)

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,].

X

Input argument: data.frame of inputs X, can be NULL

nn

Input argument: number new points in the design

Xcand

Input argument: data.frame of candidate locations Xcand

ncand

Number of rows in Xcand, i.e., nncand = dim(Xcand)[1]

fi

Vector of length nn describing the selected new design locations as indices into Xcand

XX

data.frame of selected new design locations, i.e., XX = Xcand[fi,]

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, 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

Author

Robert B. Gramacy, , and Matt Taddy,

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

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

tgp.design, lhs

Examples

#
# 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)