In this talk, we will be concerned with statistical inference for discretevalued data when modeling is based on complex generalized linear
models, such as state-space models for count data or multinomial random-
eff ect models. First, we will discuss MCMC estimation for these
types of models, which is based on an approximate, but accurate, new
mixture auxiliary sampler that introduces two sequences of artificial
latent variables. Th is mixture auxiliary sampler leads to a conditionally linear Gaussian model. Next, we will show that auxiliary mixture sampling also is useful for model choice and variable selection.