Adjustment for Data-Based Prior Selection

• Activity Number: 509
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): William Darnieder*+ and Steven MacEachern
• Companies: The Ohio State University and The Ohio State University

Abstract

In Bayesian hierarchical modeling, one often finds that little prior information is available regarding the hyperparameters. Two reasonable approaches to this problem include placing a non-informative or diffuse prior distribution on the hyperparameters, or treating the hyperparameters as fixed quantities that are estimated, as in the empirical Bayes paradigm. A third alternative is to specify a class of prior distributions from which one will be chosen based on some summary of the data. In this work, we advocate use of an insufficient statistic as this summary. We demonstrate a formal method of obtaining the posterior distribution that acknowledges that selection of the prior was conditional on a peek at the data. We establish conditions that guarantee (or conversely, violate) the propriety of the posterior distribution for a collection of common models.