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.Comment: Published in at http://dx.doi.org/10.1214/08-STS258 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
We develop an easy and direct way to define and compute the fiducial distribution of a real parameter for both continuous and discrete exponential families. Furthermore, such a distribution satisfies the requirements to be considered a confidence distribution. Many examples are provided for models, which, although very simple, are widely used in applications. A characterization of the families for which the fiducial distribution coincides with a Bayesian posterior is given, and the strict connection with Jeffreys prior is shown. Asymptotic expansions of fiducial distributions are obtained without any further assumptions, and again, the relationship with the objective Bayesian analysis is pointed out. Finally, using the Edgeworth expansions, we compare the coverage of the fiducial intervals with that of other common intervals, proving the good behaviour of the former.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.