Achieving Extra Parsimony and BMA Shrinkage via Non-Local Priors

• Activity Number: 123
• Type: Topic Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): David Rossell* and Donatello Telesca and Jairo Fuquene and Mark Steel
• Companies: University of Warwick and UCLA and University of Warwick and University of Warwick
• Keywords: model selection ; high-dimensional inference ; parameter estimation ; non-local priors ; regression models ; mixture models

Abstract

A dual challenge in high-dimensional statistics is formulate approaches that induce both model selection parsimony (to help interpret the data-generating process) and parameter estimation shrinkage (to improve prediction accuracy). Point mass priors allow not only excluding parameters from the model, hence inducing parsimony, but when combined with Bayesian model averaging (BMA) setting they also induce shrinkage. We study how adopting non-local priors (NLPs) has a dual effect of improving both parsimony and shrinkage from a theoretical and practical point of view, hence providing promising solutions for both explanatory and predictive purposes. Illustrative examples include regression, graphical and mixture model selection.