On Bayes Factors for Nonparametric
نویسنده
چکیده
In this paper we derive global Bayes factors for the comparison of a parametric model with a nonparametric alternative. The alternative is constructed by embedding the para-metric model in a mixture of Dirichlet Processes. Results include a general explicit form for partially exchangeable sequences as well as closed form expressions in the context one-way analysis of variance. Our results raise concerns on how to deene and use of Bayes factors for nonparametric alternatives. In particular, an important and disturbing corollary of our assumptions is that, when no duplicate observations occur, the Bayes factor depends on the data only through the sample size.
منابع مشابه
On the Consistency of Bayes Factors for Testing Point Null versus Nonparametric Alternatives
When testing a point null hypothesis versus an alternative that is vaguely speciied, a Bayesian test usually proceeds by putting a nonparametric prior on the alternative and then computing a Bayes factor based on the observations. This paper addresses the question of consistency, that is, whether the Bayes factor is correctly indicative of the null or the alternative as sample size increases. W...
متن کاملA Note on the Consistency of Bayes Factors for Testing Point Null versus Nonparametric Alternatives
When testing a point null hypothesis versus an alternative that is vaguely speci ed, a Bayesian test usually proceeds by putting a non-parametric prior on the alternative and then computing a Bayes factor based on the observations. This paper addresses the question of consistency, that is, whether the Bayes factor is correctly indicative of the null or the alternative as the sample size increas...
متن کاملUnobserved Heterogeneity in Longitudinal Data An Empirical Bayes Perspective
Abstract. Empirical Bayes methods for Gaussian and binomial compound decision problems involving longitudinal data are considered. A new convex optimization formulation of the nonparametric (Kiefer-Wolfowitz) maximum likelihood estimator for mixture models is used to construct nonparametric Bayes rules for compound decisions. The methods are illustrated with some simulation examples as well as ...
متن کاملBayesian Aspects of Some Nonparametric Problems
We study the Bayesian approach to nonparametric function estimation problems such as nonparametric regression and signal estimation. We consider the asymptotic properties of Bayes procedures for conjugate (=Gaussian) priors. We show that so long as the prior puts nonzero measure on the very large parameter set of interest then the Bayes estimators are not satisfactory. More specifically, we sho...
متن کامل