Building Bayesian Models Through Diagnostic Plots

• Activity Number: 368
• Type: Invited
• Date/Time: Thursday, August 15, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Graphics*
• Author(s): Steven MacEachern*+ and Mario Peruggia
• Affiliation(s): Ohio State University and Ohio State University
• Keywords: joint influence diagram ; data-splitting ; multi-party analyses

Abstract

This talk discusses elements of Bayesian model building through the use of graphical tools. A central tool, the joint influence diagram, enables us to examine how pairs of cases influence the fit of the model. The diagram serves as an exploratory technique, uncovering potential model misspecification. Additionally, more routine tools such as residual plots and probability plots are used both to assess the fit of models and to guide their development. Adhering to the notion that, when covariates are plentiful, the data rarely indicate that a single model is far superior to other candidate models, the goal of model building is to provide a collection of models that are supported by the data. Taking a Bayesian perspective, the eventual goal of model development is to produce a distribution both across models and over parameters within models. Bayesian model building has the potential to overfit the data, as a single data set may be used to select covariates, to determine the form in which they enter a model, and to provide a likelihood for computing a posterior distribution. This issue is addressed through data-splitting techniques and multi-party analyses.