Asymptotic Bayes Criteria for Nonparametric Response Surface Design

Abstract

This paper deals with Bayesian design for response surface predictionwhen the prior may be finite or infinite dimensional, the designspace arbitrary. In order that the resulting problems be manageable,we resort to asymptotic versions of D-, G- and A-optimality. Herethe asymptotics stem from allowing the error variance to be large.The problems thus elicited have strong game-like characteristics.Examples of theoretical solutions are brought forward, especiallywhen the priors are stationary processes on an interval, and we givenumerical evidence that the asymptotics work well in the finite domain.