Some Simple Data Analytic Tools for Understanding Random Field Regression Models

Abstract

Random field regression models are a popular choice for modeling data from experiments with high signal-to-noise ratios, for example computer experiments. The idea is to model the output Y from an experiment with factors X1, Xk as the realization of a Gaussian process with covariance function C(X1,..., X2). Typically the covariance function will depend on a number of unknonwn parameters that must be estimated from the data. Responses at further input settings can be estimated by their BLUP's. These models have proven successful in applications. However, they can be difficult to interpret. In this talk we show that random field regression models have a natural interpretation in terms of Bayesian response surface models. We present some simple data analytic tools that make it possible to "discover" the associated response model.