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

Authors:
Sylvia Frühwirth-Schnatter;Rudolf Frühwirth;Leonhard Held;Håvard Rue
Affiliations:
Department of Applied Statistics and Econometrics, Johannes Kepler Universität Linz, Linz, Austria;Institute of High Energy Physics, Austrian Academy of Sciences, Vienna, Austria;Institute of Social and Preventive Medicine, University of Zurich, Zurich, Switzerland;Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway
Venue:
Statistics and Computing
Year:
2009

Citing 5
Cited 5

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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.