Some Simple Data Analytic Tools for Understanding Random Field Regression Models

• Activity Number: 242
• Type: Topic Contributed
• Date/Time: Tuesday, August 13, 2002 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical & Engineering Sciences*
• Author(s): David Steinberg*+ and Dizza Bursztyn
• Affiliation(s): Tel-Aviv University and Tel-Aviv University
• Keywords: Computer experiments ; Principal Components ; Gaussian processes ; Spatial Smoothing

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 $X_1,\ldots,X_k$ as the realization of a Gaussian process with covariance function $C({\boldmath X}_1,{\boldmath X}_2)$. 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 BLUPs. 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 regression models. We present some simple data analytic tools that make it possible to "discover'' the associated regression model.