Bayesian Kernel Mixtures for Counts.

Journal Article (Journal Article)

Although Bayesian nonparametric mixture models for continuous data are well developed, there is a limited literature on related approaches for count data. A common strategy is to use a mixture of Poissons, which unfortunately is quite restrictive in not accounting for distributions having variance less than the mean. Other approaches include mixing multinomials, which requires finite support, and using a Dirichlet process prior with a Poisson base measure, which does not allow smooth deviations from the Poisson. As a broad class of alternative models, we propose to use nonparametric mixtures of rounded continuous kernels. An efficient Gibbs sampler is developed for posterior computation, and a simulation study is performed to assess performance. Focusing on the rounded Gaussian case, we generalize the modeling framework to account for multivariate count data, joint modeling with continuous and categorical variables, and other complications. The methods are illustrated through applications to a developmental toxicity study and marketing data. This article has supplementary material online.

Full Text

Duke Authors

Cited Authors

  • Canale, A; Dunson, DB

Published Date

  • December 2011

Published In

Volume / Issue

  • 106 / 496

Start / End Page

  • 1528 - 1539

PubMed ID

  • 22523437

Pubmed Central ID

  • PMC3329131

Electronic International Standard Serial Number (EISSN)

  • 1537-274X

International Standard Serial Number (ISSN)

  • 0162-1459

Digital Object Identifier (DOI)

  • 10.1198/jasa.2011.tm10552


  • eng