Defining Testing Priors from Estimation Priors via Truncation

• Activity Number: 230
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): David Rossell*+ and Donatello Telesca
• Companies: IRB Barcelona and University of California at Los Angeles
• Keywords: model selection ; estimation ; non-local prior ; posterior sampling

Abstract

Bayesians often distinguish estimation and testing priors. For testing point masses are combined with informative continuous priors, but for parameter estimation vague/improper priors seem most popular. While estimation and testing can be conciliated with decision-theoretic considerations, we argue a view from simple prior specification principles. Informative priors offer advantages for estimation, e.g. inducing regularized estimates, and are increasingly used in high-dimensional setups. Hence, we take as our starting point an informative, absolutely continuous estimation prior. To achieve a conciliation, we turn the estimation prior into a testing prior. We add point masses to capture neighborhoods around null values and truncate the continuous prior away from them. We treat the unknown truncation point as a latent variable. We provide representation theorems showing that such prior construction is equivalent to non-local priors (NLPs), a class of testing priors with good properties in high-dimensions. Besides adding intuition to the development of NLPs, our characterization facilitates extension to a wide range of models and greatly simplifies posterior sampling.