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Activity Number: 81
Type: Contributed
Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #306790
Title: Reference Posteriors from a Mixture of Reference Priors
Author(s): Michael Sonksen*+
Companies: University of New Mexico
Address: 6412 Dante Lane NW, Albuquerqeu, NM, 87114, United States
Keywords: noninformative prior ; nonparametric Bayes ; Dirichlet process ; model averaging
Abstract:

In multi-parameter settings, the reference prior for a given likelihood is not uniquely defined. Instead, the reference prior algorithm of Berger and Bernardo (1992) produces different reference priors depending on an ordering and grouping of the model parameters. In some instances, an explicit formula for all possible reference priors can be found. We define a reference posterior using a mixture of all possible reference priors. We utilize the Dirichlet process to define the prior distribution for the grouping and ordering of the parameters. The discrete nature of Dirichlet process priors makes it an ideal mixing distribution. Examination of the posterior probabilities for the various models provides insight into the viability of specific orderings and groupings. We illustrate this methodology and consider the associated computational issues with a multinomial model and a constrained Poisson rate model.


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