dmaxDesign: Maximum Entropy Designs

In DiceDesign: Designs of Computer Experiments

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=(r[i,j]):

r[i,j]=1-gamma(h[i,j])	if h[i,j] <=a,
r[i,j]=0	if if h_{ij}>a,

where h[i,j] is the distance between xi and xj, a denotes the range of the variogram and gamma is a spherical variogram:

gamma(h)= 1.5*(h/a)- 0.5*(h/a)^3 for h>=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))

Example output

       T1    T2
1   -3.51  6.74
2   -8.72  8.62
3    9.91  9.16
4   -1.48  3.54
5    9.37 -9.78
6   -5.64  1.08
7   -3.05  9.76
8   -3.81 -3.24
9  -10.00  0.36
10  -8.04 -9.23
11   5.34  5.76
12   3.94 10.00
13  -1.26 -3.20
14  -1.10 -9.54
15   5.49  1.43
16   7.71 -1.83
17   4.65 -8.42
18   1.90  7.02
19   1.98 -1.08
20  -9.12 -3.91

DiceDesign documentation built on Feb. 13, 2021, 1:06 a.m.