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

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Title: Bayesian Inference, Model Selection and Likelihood Estimation using Fast Rejection Sampling: The Conway-Maxwell-Poisson Distribution
Authors: Benson, AlanFriel, Nial
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Date: Sep-2021
Online since: 2021-11-09T12:41:56Z
Abstract: 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, a two parameter generalisation of the Poisson distribution. COM-Poisson regression modelling allows the flexibility to model dispersed count data as part of a generalised linear model (GLM) with a COM-Poisson response, where exogenous covariates control the mean and dispersion level of the response. The major difficulty with COM-Poisson regression is that the likelihood function contains multiple intractable normalising constants and is not amenable to standard inference and Markov Chain Monte Carlo (MCMC) techniques. Recent work by Chanialidis et al. (2018) has seen the development of a sampler to draw random variates from the COM-Poisson likelihood using a rejection sampling algorithm. We provide a new rejection sampler for the COM-Poisson distribution which significantly reduces the central processing unit (CPU) time required to perform inference for COM-Poisson regression models. An extension of this work shows that for any intractable likelihood function with an associated rejection sampler it is possible to construct unbiased estimators of the intractable likelihood which proves useful for model selection or for use within pseudo-marginal MCMC algorithms (Andrieu and Roberts, 2009). We demonstrate all of these methods on a real-world dataset of takeover bids.
Funding Details: Science Foundation Ireland
Type of material: Journal Article
Publisher: International Society for Bayesian Analysis
Journal: Bayesian Analysis
Volume: 16
Issue: 3
Start page: 905
End page: 931
Copyright (published version): 2021 International Society for Bayesian Analysis
Keywords: Conway-Maxwell-Poisson distributionDispersed count dataIntractable likelihoodsRejection sampling
DOI: 10.1214/20-ba1230
Language: en
Status of Item: Peer reviewed
ISSN: 1936-0975
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Appears in Collections:Mathematics and Statistics Research Collection
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