Lognormal and gamma mixed negative binomial regression

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2012-10-10

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Abstract

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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Dunson

David B. Dunson

Arts and Sciences Distinguished Professor of Statistical Science

My research focuses on developing new tools for probabilistic learning from complex data - methods development is directly motivated by challenging applications in ecology/biodiversity, neuroscience, environmental health, criminal justice/fairness, and more.  We seek to develop new modeling frameworks, algorithms and corresponding code that can be used routinely by scientists and decision makers.  We are also interested in new inference framework and in studying theoretical properties of methods we develop.  

Some highlight application areas: 
(1) Modeling of biological communities and biodiversity - we are considering global data on fungi, insects, birds and animals including DNA sequences, images, audio, etc.  Data contain large numbers of species unknown to science and we would like to learn about these new species, community network structure, and the impact of environmental change and climate.

(2) Brain connectomics - based on high resolution imaging data of the human brain, we are seeking to developing new statistical and machine learning models for relating brain networks to human traits and diseases.

(3) Environmental health & mixtures - we are building tools for relating chemical and other exposures (air pollution etc) to human health outcomes, accounting for spatial dependence in both exposures and disease.  This includes an emphasis on infectious disease modeling, such as COVID-19.

Some statistical areas that play a prominent role in our methods development include models for low-dimensional structure in data (latent factors, clustering, geometric and manifold learning), flexible/nonparametric models (neural networks, Gaussian/spatial processes, other stochastic processes), Bayesian inference frameworks, efficient sampling and analytic approximation algorithms, and models for "object data" (trees, networks, images, spatial processes, etc).




Carin

Lawrence Carin

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 Brooklyn Polytechnic Institute (now part of NYU) 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 2011-2014, and Vice Provost and Vice President for Research from 2014-2020. He was the Provost at King Abdullah University of Science & Technology (KAUST) from 2020-2023, returning to Duke in 2023. From 2003-2014 he held the William H. Younger Distinguished Professorship, and since 2018 he has held the James L. Meriam Distinguished Professorship. Dr. Carin's research focuses on machine learning (ML) and artificial intelligence (AI). He publishes widely in the main ML/AI forums, and has addressed many applications of AI, including in  medicine and security. He was co-founder of the small business Signal Innovations Group, which was acquired by BAE Systems in 2014, and in 2017 he co-founded the company Infinia ML, which was acquired by Aspirion in 2023. He is an IEEE Fellow.


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