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August 2008 Compatibility of Prior Specifications Across Linear Models
Guido Consonni, Piero Veronese
Statist. Sci. 23(3): 332-353 (August 2008). DOI: 10.1214/08-STS258

Abstract

Bayesian model comparison requires the specification of a prior distribution on the parameter space of each candidate model. In this connection two concerns arise: on the one hand the elicitation task rapidly becomes prohibitive as the number of models increases; on the other hand numerous prior specifications can only exacerbate the well-known sensitivity to prior assignments, thus producing less dependable conclusions. Within the subjective framework, both difficulties can be counteracted by linking priors across models in order to achieve simplification and compatibility; we discuss links with related objective approaches. Given an encompassing, or full, model together with a prior on its parameter space, we review and summarize a few procedures for deriving priors under a submodel, namely marginalization, conditioning, and Kullback–Leibler projection. These techniques are illustrated and discussed with reference to variable selection in linear models adopting a conventional g-prior; comparisons with existing standard approaches are provided. Finally, the relative merits of each procedure are evaluated through simulated and real data sets.

Citation

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Guido Consonni. Piero Veronese. "Compatibility of Prior Specifications Across Linear Models." Statist. Sci. 23 (3) 332 - 353, August 2008. https://doi.org/10.1214/08-STS258

Information

Published: August 2008
First available in Project Euclid: 28 January 2009

zbMATH: 1329.62331
MathSciNet: MR2483907
Digital Object Identifier: 10.1214/08-STS258

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.23 • No. 3 • August 2008
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