Bayesian Inference, Model Selection and Likelihood Estimation using Fast Rejection Sampling: The Conway-Maxwell-Poisson Distribution

Bayesian inference for models with intractable likelihood functions represents a challenging suite of problems in modern statistics. In this work we analyse the Conway-Maxwell-Poisson (COM-Poisson) distribution, two parameter generalisation Poisson distribution. COM-Poisson regression modelling allows flexibility to model dispersed count data as part generalised linear (GLM) response, where exogenous covariates control mean and dispersion level response. The major difficulty is that function contains multiple normalising constants not amenable standard Markov Chain Monte Carlo (MCMC) techniques. Recent by Chanialidis et al. (2018) has seen development sampler draw random variates from using rejection sampling algorithm. We provide new distribution which significantly reduces central processing unit (CPU) time required perform models. An extension shows any an associated it possible construct unbiased estimators proves useful selection or use within pseudo-marginal MCMC algorithms (Andrieu Roberts, 2009). demonstrate all these methods on real-world dataset takeover bids.