dmaxDesign {DiceDesign}R Documentation

Maximum Entropy Designs

Description

Space-Filling Designs with n experiments based on covariance matrix in [0,1]^d.

Usage

dmaxDesign(n, dimension, range, niter_max=1000, seed=NULL)

Arguments

n

number of experiments

dimension

number of variables

range

range of variogram

niter_max

number of iterations

seed

seed used to generate uniform design

Details

Maximum entropy design is a kind of optimal design based on Shannon's definition of entropy as the amount of information. Originally, maximum entropy sampling was proposed by Shewry and Wynn (1987). The goal of the design is to maximize the entropy defined as the determinant of the correlation matrix using a Fedorov-Mitchell exchange algorithm.

The spatial correlation matrix is defined by C=\left( \rho_{ij} \right):

\rho_{ij}=1-\gamma\left(h_{ij}\right) if h_{ij}\leq a,
\rho_{ij}=0 if h_{ij}>a,

where h_{ij} is the distance between x_{i} and x_{j}, a denotes the range of the variogram and \gamma is a spherical variogram:

\gamma(h) = 1.5 \frac{h}{a}- 0.5\left(\frac{h}{a}\right)^3 \textnormal{ for } h \leq a

Value

A list with components:

n

the number of points

design

the design of experiments

dimension

the number of variables

range

the range of the variogram

niter_mx

the number of iterations

design_init

the initial distribution

det_init

the value of the determinant for the initial distribution

det_end

the value of the determinant at the end of the procedure

seed

the value of the seed

Author(s)

J. Franco

References

Currin C., Mitchell T., Morris M. and Ylvisaker D. (1991) Bayesian Prediction of Deterministic Functions With Applications to the Design and Analysis of Computer Experiments, American Statistical Association, 86, 416, 953-963.

Shewry, M. C. and Wynn and H. P. (1987) Maximum entropy sampling, Journal of Applied Statistics 14, 165-170.

Examples

n <- 20
dimension <- 2
range <-0.9
niter_max <- 200
out <- dmaxDesign(n, dimension, range, niter_max)

## Change the dimnames, adjust to range (-10, 10) and round to 2 digits
xDRDN(out, letter = "T", dgts = 2, range = c(-10, 10))

[Package DiceDesign version 1.9 Index]