Bayesian Models for Response Surfaces. I. The Equivalence of Several Models and Their Relationship to Smoothing Splines.
Abstract
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 O'Hagan (1978) are equivalent statements. It is also showing how their models are related to the generalized smoothing splines of Wahba (1978) and to Young's (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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1984
- Accession Number
- ADA142843
Entities
People
- D. M. Steinberg
Organizations
- University of Wisconsin–Madison