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.