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Activity Number: 373
Type: Invited
Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #303719
Title: Bayesian Testing of Associations and Interactions with Multivariate Categorical Data
Author(s): David Dunson*+ and Anirban Bhattacharya
Companies: Duke University and Duke University
Address: Box 90251, Durham , NC, , USA
Keywords: Bayesian ; Nonparametrics ; Contingency table ; High-dimensional ; Genetics ; Categorical data

Massive-dimensional and enormously sparse contingency table data are routinely collected in many application areas. For example, in genetic epidemiology studies it is common to collect data on single nucleotide polymorphisms (SNPs) at many different loci along with demographic and exposure information. SNPs can be categorized as 0,1,2 while other variables are also typically categorized, leading to high-dimensional categorical data that can be organized into a contingency table. Often in epidemiology and other settings there may be high-dimensional interactions (e.g., among SNPs and among SNPs and environmental factors). Such interactions are notoriously difficult to detect and it becomes impractical to use traditional methods for contingency table analysis, such as log-linear models, since even with two-way interactions the number of terms in such models can blow up beyond the ability of current computers. Graphical modeling approaches face similar problems. To address these challenges, we propose new classes of nonparametric Bayesian models for the higher-order probability tensor characterizing the joint distribution of the categorical data. Adding to the literature on ten

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