2017/09/11 by Alan P. Benson, Nial Friel, Benson, Alan +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1709.03471
openalex publication_date 2017/09/11 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Bayesian inference for models with intractable likelihood functions\nrepresents a challenging suite of problems in modern statistics. In this work\nwe analyse the Conway-Maxwell-Poisson (COM-Poisson) distribution, a two\nparameter generalisation of the Poisson distribution. COM-Poisson regression\nmodelling allows the flexibility to model dispersed count data as part of a\ngeneralised linear model (GLM) with a COM-Poisson response, where exogenous\ncovariates control the mean and dispersion level of the response. The major\ndifficulty with COM-Poisson regression is that the likelihood function contains\nmultiple intractable normalising constants and is not amenable to standard\ninference and MCMC techniques. Recent work by Chanialidis et al. (2017) has\nseen the development of a sampler to draw random variates from the COM-Poisson\nlikelihood using a rejection sampling algorithm. We provide a new rejection\nsampler for the COM-Poisson distribution which significantly reduces the CPU\ntime required to perform inference for COM-Poisson regression models. A novel\nextension of this work shows that for any intractable likelihood function with\nan associated rejection sampler it is possible to construct unbiased estimators\nof the intractable likelihood which proves useful for model selection or for\nuse within pseudo-marginal MCMC algorithms (Andrieu and Roberts, 2009). We\ndemonstrate all of these methods on a real-world dataset of takeover bids.\n