Statistica Sinica

Toby J. Mitchell, Max D. Morris and Donald Ylvisaker^{*}

Abstract:The paper considers the problem of design for prediction of a deterministic response functionxover a domainT. A Bayesian approach is used, where the random function that represents prior uncertainty aboutxis a stationary Gaussian stochastic processX. HereT={-1,1}^{k}, the designs considered are fractional factorials, and the objective is to optimize the choice of design with respect to some criterion. The structure of stationary and of isotropic processes onTis discussed, along with the conditioning of such a process based on observation at a fractional factorial design. There are useful regularities in this, together with workable criteria on the prediction of interactions and on the prediction of unobserved values of the process.

Key words and phrases:Bayesian prediction, computer experiments, fractional factorial designs, stationary processes, two-level factors.