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

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]