Exploratory designs for computational experiments.

*(English)*Zbl 0813.62065Summary: Recent work by M. Johnson et al. [ibid. 26, 131-148 (1990)] established equivalence of the maximin distance design criterion and an entropy criterion motivated by function prediction in a Bayesian setting. The latter criterion has been used by C. Currin et al. [J. Am. Stat. Assoc. 86, 953-963 (1991)] to design experiments for which the motivating application is approximation of a complex deterministic computer model. Because computer experiments often have a large number of controlled variables (inputs), maximin designs of moderate size are often concentrated in the corners of the cuboidal design region, i.e. each input is represented at only two levels.

Here we will examine some maximin distance designs constructed within the class of Latin hypercube arrangements. The goal of this is to find designs which offer a compromise between the entropy/maximin criterion, and projective properties in each dimension (as guaranteed by Latin hypercubes). A simulated annealing search algorithm is presented for constructing these designs, and patterns apparent in the optimal designs are discussed.

Here we will examine some maximin distance designs constructed within the class of Latin hypercube arrangements. The goal of this is to find designs which offer a compromise between the entropy/maximin criterion, and projective properties in each dimension (as guaranteed by Latin hypercubes). A simulated annealing search algorithm is presented for constructing these designs, and patterns apparent in the optimal designs are discussed.

##### MSC:

62K05 | Optimal statistical designs |

65C99 | Probabilistic methods, stochastic differential equations |

62F15 | Bayesian inference |

##### Keywords:

interpolation; random functions; computer experiments; maximin distance designs; Latin hypercube arrangements; entropy/maximin criterion; simulated annealing search algorithm
PDF
BibTeX
XML
Cite

\textit{M. D. Morris} and \textit{T. J. Mitchell}, J. Stat. Plann. Inference 43, No. 3, 381--402 (1995; Zbl 0813.62065)

Full Text:
DOI

##### References:

[1] | Bohachevsky, I.O.; Johnson, M.E.; Stein, M.L., Generalized simulated annealing for function optimization, Technometrics, 28, 209-217, (1986) · Zbl 0609.65045 |

[2] | Box, G.E.P.; Meyer, R.D., An analysis for unreplicated fractional factorials, Technometrics, 28, 11-18, (1986) · Zbl 0586.62168 |

[3] | Currin, C.; Mitchell, T.; Morris, M.; Ylvisaker, D., Bayesian prediction deterministic functions, with applications to the design and analysis of computer experiments, J amer. statist. assoc., 86, 953-963, (1991) |

[4] | Johnson, M.; Moore, L.; Ylvisaker, D., Minimax and maxmin distance designs, J. statist. plann. inference, 26, 131-148, (1990) |

[5] | Kimeldorf, G.S.; Wahba, G., Spline functions and stochastic processes, Sankhya ser. A, 32, 173-180, (1970) · Zbl 0226.60064 |

[6] | McKay, M.D.; Conover, W.J.; Beckman, R.J., A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21, 239-245, (1979) · Zbl 0415.62011 |

[7] | Micchelli, C.A.; Wahba, G., Design problems for optimal surface interpolation, () |

[8] | Morris, M.D.; Mitchell, T.J., Exploratory designs for computational experiments, (1992), available from National Technical Information Service 5285 Port Royal Road, Springfield, VA 22161, ORNL/TM-12045 |

[9] | Morris, M.D.; Mitchell, T.J.; Ylvisaker, D., Bayesian design and analysis of computer experiments: use of derivatives in surface prediction, Technometrics, 35, 243-255, (1993) · Zbl 0785.62025 |

[10] | Park, J.-S., Tuning complex computer codes to data and optimal designs, (), (unpublished) |

[11] | Patterson, H.D., The errors of lattice sampling, J. roy. statist. soc. ser. B, 16, 140-149, (1954) · Zbl 0056.38101 |

[12] | Sacks, J.; Welch, W.J.; Mitchell, T.J.; Wynn, H.P., Design and analysis of computer experiments, Statist. sci., 4, 409-423, (1989) · Zbl 0955.62619 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.