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AIC Seminar Series

Bayesian Model Specification

David DraperUniversity of California, Santa Cruz[Home Page]

Notice:  hosted by Sugato Basu

Date:  2006-06-14 at 10:30

Location:  EJ228  (Directions)

   Abstract

A standard (data-analytic) approach to statistical model specification, practiced with equal vigor by Bayesians and non-Bayesians alike, involves the initial choice, for the structure of the model, of one or another of a variety of standard parametric families, followed by modification of this initial choice – once data begin to arrive – if the data suggest deficiencies in the original specification.

In this talk (a) I will argue that this approach is formally incoherent, because it amounts to using the data both to specify the prior distribution on structure space and to update using this data-determined prior; (b) I will identify two approaches to avoiding (at least in principle, and with a fair amount of data) the incoherence in (a) – (1) Bayesian nonparametric modeling and (2) three-way out-of-sample predictive validation; (c) I will provide details on implementing (2); (d) I will argue that to make progress in coherent Bayesian model specification in complicated problems you have to either implicitly or explicitly choose a utility structure which defines, for you, when the model currently being examined is good enough; (e) I will argue that it is best to make this choice explicitly on the basis of real-world considerations regarding the use to which the model will be put; and (f) I will contrast model selection methods based on the log score and deviance information criteria (DIC) as two examples of (e) with utilities governed by predictive accuracy. This is joint work with a former Ph.D. student, Milovan Krnjajic.

Keywords: Bayesian model specification, DIC, model selection as a decision problem, predictive log scoring rule, three-way out-of-sample predictive validation, Bayesian nonparametric modeling

   Bio for David Draper

David Draper is a Professor in, and Chair of, the Department of Applied Mathematics and Statistics in the Baskin School of Engineering at the University of California, Santa Cruz. From 2001 to 2003 he served as the President-Elect, President, and Past President of the International Society for Bayesian Analysis (ISBA). His research is in the areas of Bayesian inference and prediction, model uncertainty and empirical model-building, hierarchical modeling, Markov Chain Monte Carlo methods, and Bayesian nonparametric methods, with applications mainly in medicine, health policy, education, and environmental risk assessment. He has a particular interest in the exposition of complex statistical methods and ideas in the context of real-world applications.

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