The Ubiquity of Information Inconsistency in Testing and Model Selection

• Activity Number: 432
• Type: Invited
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): James O. Berger*+ and M. J. Bayarri and Joris Mulder
• Companies: Duke University and University of Valencia and Tilburg University
• Keywords: Model Uncertainty ; Hypothesis Testing ; Information Inconsistency ; Conjugate Priors ; Bayes Factors

Abstract

Information inconsistency refers to the scenario in which the data seems to provide compelling evidence for a hypothesis or model (e.g., a huge value of the t-statistic in testing whether or not a normal mean is zero), and yet the Bayesian analysis does not suggest that there is compelling evidence. This has long been thought to be somewhat of a curiosity, arising only with special choices of prior distributions. The truth of the matter is quite different; information inconsistency is the rule, rather than the exception, for Bayesian testing and model selection and occurs with many of the most common choices of priors, both proper and improper. The talk will discuss why this is so and what it implies in terms of strategies for selecting testing and model selection priors.