Statistical Inference for Intractable Count Distributions

MCMC is widely used for Bayesian inference, but standard methods struggle with intractable normalising constants in some models. These intractable constants appear in the posterior and complicate the acceptance probability in MCMC. The text illustrates the challenge using distributions like the Double Poisson, COM-Poisson, and Zipf. Specialised methods such as the exchange algorithm, auxiliary variable methods, pseudo-marginal MCMC, etc., have been developed to overcome these issues, but none with guaranteed accuracy.. Here we study ways to accurately evaluate the normalisation constant for MCMC methods. And we present a previous result with COM-Poisson.