Bayesian generalized product partition model
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Starting with a carefully formulated Dirichlet process (DP) mixture model, we derive a generalized product partition model (GPPM) in which the partition process is predictor-dependent. The GPPM generalizes DP clustering to relax the exchangeability assumption through the incorporation of predictors, resulting in a generalized Pólya urn scheme. In addition, the GPPM can be used for formulating flexible semiparametric Bayes models for conditional distribution estimation, bypassing the need for expensive computation of large numbers of unknowns characterizing priors for dependent collections of random probability measures. A variety of special cases are considered, and an efficient Gibbs sampling algorithm is developed for posterior computation. The methods are illustrated using simulation examples and an epidemiologic application.
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Arts and Sciences Distinguished Professor of Statistical Science
Development of novel approaches for representing and analyzing complex data. A particular focus is on methods that incorporate geometric structure (both known and unknown) and on probabilistic approaches to characterize uncertainty. In addition, a big interest is in scalable algorithms and in developing approaches with provable guarantees.This fundamental work is directly motivated by applications in biomedical research, network data analysis, neuroscience, genomics, ecol