Bayesian Variable Selection in Multinomial Probit Models with Application to Spectral Data and DNA Microarray

• Activity Number: 283
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Stat. Sciences*
• Author(s): Naijun Sha*+ and Marina Vannucci and Philip Brown
• Affiliation(s): Texas A&M University and Texas A&M University and University of Kent
• Keywords: Bayesian variable selection ; latent variables ; MCMC ; multinomial probit model ; truncated sampling ; microarrays

Abstract

Here we focus on classification problems, where the number of predictors substantially exceeds the sample size, and propose a Bayesian variable selection approach to multinomial probit models. Motivated by the binary model with latent variables, we consider multivariate extensions to the case of more than two categories and use latent variables to specialize the general distributional setting to the linear model with Gaussian errors. We then apply Bayesian variable selection techniques that use natural conjugate prior distributions. A posteriori we perform inference on the marginal distribution of single models using MCMC methods and truncated normal and student-t sampling techniques to draw multivariate vectors.

We present applications both in chemometrics and in functional genomics, first to a dataset with three wheat varieties and 100 near infra-red absorbances as regressors, then to the data of Golub {\it et al.} (1999) on cancer classification based on microarray data, and to a dataset not previously analyzed by other authors that involves 755 genes and two treatments.