Compatibility of prior specifications across linear models

Guido Consonni, Piero Veronese

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

29 Citazioni (Scopus)

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.
Lingua originaleEnglish
pagine (da-a)332-353
Numero di pagine22
RivistaStatistical Science
Volume23
DOI
Stato di pubblicazionePubblicato - 2008

Keywords

  • Compatible prior
  • Kullback-Leibler projection

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