Showing papers by "James O. Berger published in 1996"
TL;DR: This article introduces a new criterion called the intrinsic Bayes factor, which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual Bayes factors.
Abstract: In the Bayesian approach to model selection or hypothesis testing with models or hypotheses of differing dimensions, it is typically not possible to utilize standard noninformative (or default) prior distributions. This has led Bayesians to use conventional proper prior distributions or crude approximations to Bayes factors. In this article we introduce a new criterion called the intrinsic Bayes factor, which is fully automatic in the sense of requiring only standard noninformative priors for its computation and yet seems to correspond to very reasonable actual Bayes factors. The criterion can be used for nested or nonnested models and for multiple model comparison and prediction. From another perspective, the development suggests a general definition of a “reference prior” for model comparison.
993 citations
TL;DR: In this paper, hierarchical priors for normal means are categorized in terms of admissibility and inadmissibility of resulting estimators for a quite general scenario, and the conditions under which the (generally improper) priors result in proper posteriors.
Abstract: In hierarchical Bayesian modeling of normal means, it is common to complete the prior specification by choosing a constant prior density for unmodeled hyperparameters (e.g., variances and highest-level means). This common practice often results in an inadequate overall prior, inadequate in the sense that estimators resulting from its use can be inadmissible under quadratic loss. In this paper, hierarchical priors for normal means are categorized in terms of admissibility and inadmissibility of resulting estimators for a quite general scenario. The Jeffreys prior for the hyper-variance and a shrinkage prior for the hypermeans are recommended as admissible alternatives. Incidental to this analysis is presentation of the conditions under which the (generally improper) priors result in proper posteriors.
89 citations
01 Jan 1996
TL;DR: In this article, the default Bayes factor with a (sensible) prior is compared to the intrinsic prior with proper priors, in the sense of being "predictively matched".
Abstract: In Bayesian model selection or hypothesis testing, it is difficult to develop default Bayes factors, since (improper) noninformative priors cannot typically be used. In developing such default Bayes factors, we feel that it is important to keep several principles in mind. The first is that the default Bayes factor should correspond, in some sense, to an actual Bayes factor with a (sensible) prior, which we call an intrinsic prior. The second principle is that such priors should be properly calibrated across models, in the sense of being “predictively matched.” These notions will be described and illustrated, primarily using examples involving the intrinsic Bayes factor, a recently proposed default Bayes factor. It will be seen that intrinsic Bayes factors seem to correspond to actual Bayes factors with proper priors, at least for nested model scenarios. The corresponding intrinsic priors are specifically given for the normal linear model.
38 citations
Cornell University1, Charles III University of Madrid2, Technical University of Madrid3, University of Granada4, Purdue University5, University College London6, Duke University7, University of British Columbia8, Carnegie Mellon University9, University of Texas at Austin10, Stanford University11, University of Chicago12, University of Rouen13, University of Valencia14, Pennsylvania State University15, University of Michigan16
TL;DR: This review article looks at a small part of the picture of the interrelationship between statistical theory and computational algorithms, especially the Gibbs sampler and the Accept-Reject algorithm, paying particular attention to how the methodologies affect and complement each other.
Abstract: This review article looks at a small part of the picture of the interrelationship between statistical theory and computational algorithms, especially the Gibbs sampler and the Accept-Reject algorithm. We pay particular attention to how the methodologies affect and complement each other.
31 citations