Bayes Multiple Decision Functions

• Activity Number: 349
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Wensong Wu*+ and Edsel A. Pena
• Companies: University of South Carolina and University of South Carolina
• Keywords: Bayes decision function ; multiple testing ; high-dimensional data ; dependent data ; Sequential Monte Carlo ; failure-time data

Abstract

In this paper, a general form of Bayes multiple decision functions (BMDF) with respect to a class of cost-weighted loss functions is presented. An algorithm of finding the BMDF is provided based upon posterior expectations. In particular, loss functions such as false discovery proportion (fdp), false nondiscovery proportion (fnp), and missed discovery proportion (mdp) are considered. Results are applicable in many settings including multiple hypothesis testing, multiple classification and prediction, and high-dimensional variable selection. A dependent data structure is allowed and is modeled through a class of frailty-induced Archimedean copulas. In particular, non-Gaussian dependent data structure is of interest, especially in settings with failure-time data. Computation of the posterior expectations is facilitated by using Sequential Monte Carlo (SMC) algorithms.