WITHDRAWN: Bayesian Variable Selection for Correlated Multivariate Data

• Activity Number: 384
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Kyu Ha Lee and Mahlet Tadesse and Brent Coull
• Companies: Harvard School of Public Health and Georgetown University and Harvard School of Public Health
• Keywords: Bayesian variable selection ; Ising model ; Markov chain Monte Carlo ; Phase transition

Abstract

We consider the problem of multivariate variable selection for regression models where only a subset of response variables is affected by some covariates but not others. The statistical modeling for this problem becomes more challenging when there exist significant correlations between multivariate outcomes that must be taken into account for variable selection. In this paper, we propose a Bayesian framework for the analysis of multivariate data where outcome variables and covariates might be of high-dimension. For variable selection, the spike-slab prior is used for regression parameters and it is assumed to depend on the indicator binary parameters. While iid Bernoulli distribution is traditionally used as the prior for indicator parameters, we devise a special prior that can incorporate the correlations of the response variables predicted by our proposed model into the selection of relevant covariates associated with some response variables. To implement our methodology, we develop an efficient Markov chain Monte Carlo (MCMC) algorithm. The superiority of our method over standard stochastic search variable selection model is demonstrated via simulation studies.