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

DC FieldValueLanguage
dc.contributor.authorBenson, Alan-
dc.contributor.authorFriel, Nial-
dc.date.accessioned2021-11-09T12:41:56Z-
dc.date.available2021-11-09T12:41:56Z-
dc.date.copyright2021 International Society for Bayesian Analysisen_US
dc.date.issued2021-09-
dc.identifier.citationBayesian Analysisen_US
dc.identifier.issn1936-0975-
dc.identifier.urihttp://hdl.handle.net/10197/12594-
dc.description.abstractBayesian 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.en_US
dc.description.sponsorshipScience Foundation Irelanden_US
dc.language.isoenen_US
dc.publisherInternational Society for Bayesian Analysisen_US
dc.subjectConway-Maxwell-Poisson distributionen_US
dc.subjectDispersed count dataen_US
dc.subjectIntractable likelihoodsen_US
dc.subjectRejection samplingen_US
dc.titleBayesian Inference, Model Selection and Likelihood Estimation using Fast Rejection Sampling: The Conway-Maxwell-Poisson Distributionen_US
dc.typeJournal Articleen_US
dc.internal.authorcontactothernial.friel@ucd.ieen_US
dc.statusPeer revieweden_US
dc.identifier.volume16en_US
dc.identifier.issue3en_US
dc.identifier.startpage905en_US
dc.identifier.endpage931en_US
dc.identifier.doi10.1214/20-ba1230-
dc.neeo.contributorBenson|Alan|aut|-
dc.neeo.contributorFriel|Nial|aut|-
dc.date.updated2020-09-15T11:04:30Z-
dc.identifier.grantid12/IP/1424-
dc.identifier.grantid12/RC/2289_P2-
dc.rights.licensehttps://creativecommons.org/licenses/by/3.0/ie/en_US
item.fulltextWith Fulltext-
item.grantfulltextopen-
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