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

The article proposes an improved method of auxiliary mixture sampling for count data, binomial data and multinomial data. In constrast to previously proposed samplers the method uses a limited 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 smaller number of latent variables results in a more general error distribution, which is a negative log-Gamma distribution with arbitray 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 on two epidemiological case studies.