TWO-LEVEL FRACTIONAL FACTORIALS AND BAYESIAN PREDICTION

The paper considers the problem of design for prediction of a deterministic response function x over a domain T . A Bayesian approach is used, where the random function that represents prior uncertainty about x is a stationary Gaussian stochastic process X. Here T = f 1; 1g, 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 on T is 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.