Improved auxiliary mixture sampling for hierarchical models of non-Gaussian data

Sylvia Frühwirth-Schnatter*, Rudolf Frühwirth, Leonhard Held, Haavard Rue

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

Abstract

The article considers Bayesian analysis of hierarchical models for count, binomial and multinomial data using efficient MCMC sampling procedures. To this end, an improved method of auxiliary mixture sampling is proposed. In contrast to previously proposed samplers the method uses a bounded number of latent variables per observation, independent of the intensity of the underlying Poisson process in the case of count data, or of the number of experiments in the case of binomial and multinomial data. The bounded number of latent variables results in a more general error distribution, which is a negative log-Gamma distribution with arbitrary integer shape parameter. The required approximations of these distributions by Gaussian mixtures have been computed. Overall, the improvement leads to a substantial increase in efficiency of auxiliary mixture sampling for highly structured models. The method is illustrated for finite mixtures of generalized linear models and an epidemiological case study.

Original languageEnglish (US)
Pages (from-to)479-492
Number of pages14
JournalStatistics and Computing
Volume19
Issue number4
DOIs
StatePublished - Jan 1 2009

Keywords

  • Binomial data
  • Count data
  • Finite mixture models
  • Gaussian mixture
  • Log-Gamma distribution
  • Multinomial data
  • Negative binomial distribution

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics

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