## Bayesian Models for Response Surfaces and Their Implications for Experimental Design |

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### Contents

Introduction 1 | vi |

Bayesian Response Surface Models | 19 |

Bayesian Estimates of the Response Surface | 35 |

11 other sections not shown

### Common terms and phrases

approach approximating model approximating polynomial assumed assumptions average Bayesian models bias covariance function bias term Blight and Ott Chapter choice classical optimal design classical response surface converges corresponds covariance matrix D-optimal defined degree polynomial denote design points design region diffuse prior efficiency experimental design experimental error experimental region experimental runs explanatory variables Fourier series Gaussian stochastic process given graduating function Hermite polynomials improper prior Kalman filter Kiefer lack of fit least squares Lemma Lindley and Smith linear model Mehler's formula minimal O'Hagan observed data optimal design theory optimality criteria orthogonal polynomials posterior variance precisely prediction equation prior distribution prior variances problem Proof region of interest regression coefficients regression model regression parameters regressor response surface experiments response surface methodology response surface models response surface studies spline standard statistical suggested sum of squares temperature Theorem true response function vague prior distribution VarJY vector weight function