The paper reviews recent advances in analyzing complex count, data models using computer intensive Bayesian methods, such as (Jibbs sampling; or Markov Chain Monte Carlo. These methods provide a powerful estimation tool for models characterized by an underlying latent; .st.ruct.un'. Examples are count data with random effects, correlated count data, counteifacUials in treatment models, latent class models, endogenous switching models and models with underreporting, to name but a few. In all of these cases, the Bayesian approach can be implemented by a simple extension of the parameter space to include the latent effects, a ca.se of data augmentation. As a by-product of the MCMC simulation, the posterior distribution of the latent elfecls i.s obtained, which may be very useful in some problems.
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