JSM 2005 - Toronto

Abstract #302588

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 114
Type: Invited
Date/Time: Monday, August 8, 2005 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #302588
Title: Some Bayesian Perspectives on Combining Models
Author(s): Merlise Clyde*+ and Edwin Iversen and Jennifer Pittman and Rosy Luo
Companies: Duke University and Duke University and Duke University and Duke University
Address: Box 90251 Old Chemistry Room 223E, Durham, NC, 27708-0251,
Keywords: Model Averaging ; CART ; Gene Expression ; Decision Theory
Abstract:

Consideration of multiple models is routine in statistical practice. With computational advances over the past decade, there has been increased interest in methods for making inferences based on combining models. Examples include boosting, bagging, stacking, and Bayesian Model Averaging (BMA), which often lead to improved performance over methods based on selecting a single model. Bernardo and Smith have described two Bayesian frameworks for model selection known as the M-closed and M-open perspectives. The standard formulation of Bayesian Model Averaging arises as an optimal solution for combining models in the M-closed perspective, where one believes that the ``true'' model is included in the list of models under consideration. In the M-open perspectives, the ``true'' model is outside the space of models to be combined, so that model averaging using posterior model probabilities is no longer applicable. Using a decision theoretic approach, we present optimal Bayesian solutions for combining models in both frameworks. We illustrate the methodology with an example of combining models representing two distinct classes.

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Revised March 2005