Fall Seminar Series - October 30, 2003
University of Minnesota
School of Statistics
College of Liberal Arts

Bayesian Tools for EDA and Model Building

Mario Peruggia
Department of Statistics
The Ohio State University

Thursday, October 30, 2003
4:00 PM, 115 Ford Hall
Minneapolis, East Bank Campus
Social at 3:30 PM, 300 Ford Hall

Abstract

  Hierarchical Bayes models provide a natural way of incorporating covariate information into the inferential process through the elaboration of regression equations for one or more of the model parameters, with errors that are often assumed to be i.i.d. Gaussian. Unfortunately, building adequate regression models is a complicated art form that requires the practitioner to make numerous decisions along the way. Assessing the validity of the modeling decisions is often difficult.

In the first half of this talk, I consider a strategy for Bayesian model building that begins by fitting a simple, default model to the data. Numerical and graphical exploratory tools, based on summary quantities from the default fit, are used to assess the adequacy of the initial model and to identify directions in which the fit can be refined. I apply this strategy to build a Bayesian regression model for a classic set of data on brain and body weights of mammalian species and discover inadequacies in the traditional regression model through use of the proposed exploratory tools.

In the second half of the talk I illustrate another device for ascertaining the quality of the modeling choices. I specify a time series structure in the probability model for the errors that incorporates the i.i.d. model as a special case. Severe departures from independence can be detected by examining the posterior distribution of the parameters of the time series. Strong dependencies provide evidence that some other aspects (typically conditional means) of the model have been misspecified. I illustrate the methodology through several examples including its application to the analysis of the data on brain and body weights of mammalian species.

The first half of the talk is based on joint work with Steven MacEachern.