Bayesian Prediction of Deterministic Functions, with Applications to the Design and Analysis of Computer Experiments

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Abstract
This article is concerned with prediction of a function y(t) over a (multidimensional) domain T, given the function values at a set of “sites” {t (1), t (2), …, t (n)} in T, and with the design, that is, with the selection of those sites. The motivating application is the design and analysis of computer experiments, where t determines the input to a computer model of a physical or behavioral system, and y(t) is a response that is part of the output or is calculated from it. Following a Bayesian formulation, prior uncertainty about the function y is expressed by means of a random function Y, which is taken here to be a Gaussian stochastic process. The mean of the posterior process can be used as the prediction function ŷ(t), and the variance can be used as a measure of uncertainty. This kind of approach has been used previously in Bayesian interpolation and is strongly related to the kriging methods used in geostatistics. Here emphasis is placed on product linear and product cubic correlation func...

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