Bayesian Models for Response Surfaces of Uncertain Functional Form.

摘要

Experimental response functions are often approximated by simple empirical functions such as polynomials. Several methods for modeling such responses which take into account this approximate nature are described and are shown to be essentially equivalent. The models all involve a Bayesian analysis which reflects prior experimnetal belief about the ability of the empirical approximation to represent the true response function. The models are also related to Kalman filters. Implications of the models for statistical inference are examined with particular attention to estimating the response function. Numerical examples help illustrate the models. A general predictive check is developed to examine the consistency of model with the observed data.