Bayesian Models for Response Surfaces. I. The Equivalence of Several Models and Their Relationship to Smoothing Splines.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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In response surface modeling, simple graduating functions such as low-degree polynomials are used to approximate complex, unknown response functions. Several authors have suggested Bayesian generalizations of response surface models that incorporate prior belief as to the in adequacy of a graduating function to represent a response function. The author shows that the models of Smith 1973, Blight and Ott 1975, and OHagan 1978 are equivalent statements. It is also showing how their models are related to the generalized smoothing splines of Wahba 1978 and to Youngs 1977 proposal for Bayesian polynomial regression. Finally, the author suggests a canonical representation of the models in terms of generalized Fourier series expansions of the response function and show how such expansions can be used to develop reasonable prior distributions. Author
- Statistics and Probability