Compatibility of prior specifications across linear models

By Guido Consonni, Piero Veronese. 2008

61 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2bb44c64b5c23bafed98526d0b437dda9ebda637

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Citations in the corpus

Bayesian hypothesis testing for psychologists: a tutorial on the Savage-Dickey method. (2010, unknown): “The first disadvantage is that it is implicitly assumed that the common nuisance parameters fulfill exactly the same roles, whether they are part of H0 or H1; some people believe this assumption is too strict (for a discussion see Consonni & Veronese, 2008).”
Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors (2014, methodology): “Given the prior distribution on the parameter space of a full encompassing model, Consonni and Veronese (2008) used Kullback–Leibler projection, in the context of Bayesian model comparison, to derive suitable prior distributions for candidate submodels.”