Objective Bayes Variable Selection for Well-Formulated Models

• Activity Number: 676
• Type: Topic Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Daniel Taylor Rodriguez*+ and Nikolay Bliznyuk and Linda Young and Andrew Womack
• Companies: University of Florida and University of Florida and University of Florida and University of Florida
• Keywords: well-formulated models ; stochastic search algorithm ; objective Bayesian model selection ; Bayes Factors for Intrinsic Priors ; Model priors

Abstract

In the variable selection problem where relationships between the predictors are present, the resulting model selection is not invariant to coding transformations when certain lower order terms are excluded. Restricting the model search to the space of well formulated models helps guard against these difficulties. Well formulated models are those that include all the lower order terms associated to the higher order terms present in a polynomial model. With this in mind we develop a stochastic search algorithm -using Bayes factors for Intrinsic Priors- which is restricted to the subspace of well formulated models. This is done by formulating model priors that block the paths to models that are not well defined, in contrast to the commonly used uniform model priors. We propose two different flavors of the algorithm; the first one assumes more observations than covariates, while the second one can be used even when this is not the case.