Bayesian Inference, Model Selection and Likelihood Estimation using Fast Rejection Sampling: The Conway-Maxwell-Poisson Distribution
|Title:||Bayesian Inference, Model Selection and Likelihood Estimation using Fast Rejection Sampling: The Conway-Maxwell-Poisson Distribution||Authors:||Benson, Alan; Friel, Nial||Permanent link:||http://hdl.handle.net/10197/12594||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 distribution; Dispersed count data; Intractable likelihoods; Rejection sampling||DOI:||10.1214/20-ba1230||Language:||en||Status of Item:||Peer reviewed||ISSN:||1936-0975||This item is made available under a Creative Commons License:||https://creativecommons.org/licenses/by/3.0/ie/|
|Appears in Collections:||Mathematics and Statistics Research Collection|
Insight Research Collection
Show full item record
If you are a publisher or author and have copyright concerns for any item, please email firstname.lastname@example.org and the item will be withdrawn immediately. The author or person responsible for depositing the article will be contacted within one business day.