Bayes and empirical Bayes: do they merge?

Details Bayes and empirical Bayes: do they merge? Bayes and empirical Bayes: do they merge?

2012-04-06

arxiv.org/abs/1204.1470v1

Mathematics

Statistics Theory

27 pages

Scientific paper

Bayesian inference is attractive for its coherence and good frequentist properties. However, it is a common experience that eliciting a honest prior may be difficult and, in practice, people often take an {\em empirical Bayes} approach, plugging empirical estimates of the prior hyperparameters into the posterior distribution. Even if not rigorously justified, the underlying idea is that, when the sample size is large, empirical Bayes leads to "similar" inferential answers. Yet, precise mathematical results seem to be missing. In this work, we give a more rigorous justification in terms of merging of Bayes and empirical Bayes posterior distributions. We consider two notions of merging: Bayesian weak merging and frequentist merging in total variation. Since weak merging is related to consistency, we provide sufficient conditions for consistency of empirical Bayes posteriors. Also, we show that, under regularity conditions, the empirical Bayes procedure asymptotically selects the value of the hyperparameter for which the prior mostly favors the "truth". Examples include empirical Bayes density estimation with Dirichlet process mixtures.

Affiliated with

Also associated with

No associations

Rating

Bayes and empirical Bayes: do they merge? does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bayes and empirical Bayes: do they merge?, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bayes and empirical Bayes: do they merge? will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-184651