Bayesian Models for Response Surfaces. II. Estimating the Response Surface

摘要

We analyze a Bayesian model for response surfaces. This model augments a simple graduating function with a bias term that represents the difference between the true, but unknown, response function and the graduating function. The model is a straightforward extension of Blight and Ott's (1975) Bayesian model for polynomial regression. The bias term is defined in terms of prior distributions and we show how estimates of the response surface and measures of precision depend on the form of the prior distribution. Estimates and measures of precision are given for strictly proper prior distributions and also when improper priors are assigned to the coefficients of the graduating function, in which case the model leads to generalized spline estimates. (Author)