Maximum Entropy Designs
Space-Filling Designs with n experiments based on covariance matrix in [0,1]^d.
dmaxDesign(n, dimension, range, niter_max=1000, seed=NULL)
n |
number of experiments |
dimension |
number of variables |
range |
range of variogram |
niter_max |
number of iterations |
seed |
seed used to generate uniform design |
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.
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
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.
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))
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