Lognormal and gamma mixed negative binomial regression
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In regression analysis of counts, a lack of simple and efficient algorithms for posterior computation has made Bayesian approaches appear unattractive and thus underdeveloped. We propose a lognormal and gamma mixed negative binomial (NB) regression model for counts, and present efficient closed-form Bayesian inference; unlike conventional Poisson models, the proposed approach has two free parameters to include two different kinds of random effects, and allows the incorporation of prior information, such as sparsity in the regression coefficients. By placing a gamma distribution prior on the NB dispersion parameter r, and connecting a log-normal distribution prior with the logit of the NB probability parameter p, efficient Gibbs sampling and variational Bayes inference are both developed. The closed-form updates are obtained by exploiting conditional conjugacy via both a compound Poisson representation and a Polya-Gamma distribution based data augmentation approach. The proposed Bayesian inference can be implemented routinely, while being easily generalizable to more complex settings involving multivariate dependence structures. The algorithms are illustrated using real examples. Copyright 2012 by the author(s)/owner(s).
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James L. Meriam Distinguished Professor of Electrical and Computer Engineering
Lawrence Carin earned the BS, MS, and PhD degrees in electrical engineering at the University of Maryland, College Park, in 1985, 1986, and 1989, respectively. In 1989 he joined the Electrical Engineering Department at Polytechnic University (Brooklyn) as an Assistant Professor, and became an Associate Professor there in 1994. In September 1995 he joined the Electrical and Computer Engineering (ECE) Department at Duke University, where he is now a Professor. He was ECE Department Chair from 2011
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
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