Lognormal and gamma mixed negative binomial regression

Zhou, M

Li, L

Dunson, D

Carin, L

2014-07-22T16:19:35Z

2012-10-10

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).

https://hdl.handle.net/10161/8954

icml.cc / Omnipress

Proceedings of the 29th International Conference on Machine Learning, ICML 2012

Lognormal and gamma mixed negative binomial regression

Journal article

1343

1350

Duke

Duke Institute for Brain Sciences

Electrical and Computer Engineering

Institutes and Provost's Academic Units

Mathematics

Pratt School of Engineering

Statistical Science

Trinity College of Arts & Sciences

University Institutes and Centers

Published

2