Objective Bayesian Graphical Model Selection with Bayes Factors Based on Test Statistics and Nonlocal Alternative Priors: How Do Interactions of DNA Components Lead to a Disease?

• Activity Number: 559
• Type: Contributed
• Date/Time: Thursday, August 6, 2009 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Adarsh Joshi*+ and Jianhua Hu and Valen E. Johnson
• Companies: The University of Texas M.D. Anderson Cancer Center and The University of Texas M.D. Anderson Cancer Center and The University of Texas M.D. Anderson Cancer Center
• Keywords: Bayesian Graphs ; Bayes Factors ; MCMC ; Non-local alternative priors ; Objective Bayesian Analysis ; Bayesian Model Selection

Abstract

Bayesian methods are often criticized on the grounds of subjectivity. Furthermore, misspecified priors can have a deleterious effect on Bayesian inference. Noting that model selection is effectively a test of many hypotheses, the co-authors have in their previous research sought to eliminate the need of prior specification by computing Bayes Factors from Frequentist test statistics. In the current work, we have extended this line of thought by replacing local alternative priors with non-local alternative priors to enable greater separation between the theories of null and alternative hypotheses. Furthermore, a novel MCMC based methodology has been developed to incorporate Bayes Factors in Graphical model selection. Efficient FORTRAN code has made it possible to apply the methodology to graphs with hundreds of nodes. Our applications include discretized gene expression data and SNP data.