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dc.contributor.authorPiancastelli, Luiza S. C.
dc.contributor.authorFriel, Nial
dc.contributor.authorBarreto-Souza, Wagner
dc.contributor.authorOmbao, Hernando
dc.date.accessioned2021-07-26T11:52:36Z
dc.date.available2021-07-26T11:52:36Z
dc.date.issued2021-07-15
dc.identifier.urihttp://hdl.handle.net/10754/670284
dc.description.abstractIn this paper, a multivariate count distribution with Conway-Maxwell (COM)-Poisson marginals is proposed. To do this, we develop a modification of the Sarmanov method for constructing multivariate distributions. Our multivariate COM-Poisson (MultCOMP) model has desirable features such as (i) it admits a flexible covariance matrix allowing for both negative and positive non-diagonal entries; (ii) it overcomes the limitation of the existing bivariate COM-Poisson distributions in the literature that do not have COM-Poisson marginals; (iii) it allows for the analysis of multivariate counts and is not just limited to bivariate counts. Inferential challenges are presented by the likelihood specification as it depends on a number of intractable normalizing constants involving the model parameters. These obstacles motivate us to propose a Bayesian inferential approach where the resulting doubly-intractable posterior is dealt with via the exchange algorithm and the Grouped Independence Metropolis-Hastings algorithm. Numerical experiments based on simulations are presented to illustrate the proposed Bayesian approach. We analyze the potential of the MultCOMP model through a real data application on the numbers of goals scored by the home and away teams in the Premier League from 2018 to 2021. Here, our interest is to assess the effect of a lack of crowds during the COVID-19 pandemic on the well-known home team advantage. A MultCOMP model fit shows that there is evidence of a decreased number of goals scored by the home team, not accompanied by a reduced score from the opponent. Hence, our analysis suggests a smaller home team advantage in the absence of crowds, which agrees with the opinion of several football experts.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/pdf/2107.07561.pdf
dc.rightsArchived with thanks to arXiv
dc.subjectBayesian inference
dc.subjectConway-Maxwell-Poisson distribution
dc.subjectExchange algorithm
dc.subjectPseudomarginal Monte Carlo
dc.subjectMultivariate count data
dc.subjectThermodynamic integration
dc.titleMultivariate Conway-Maxwell-Poisson Distribution: Sarmanov Method and Doubly-Intractable Bayesian Inference
dc.typePreprint
dc.contributor.departmentStatistics Program, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
dc.contributor.departmentStatistics Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.eprint.versionPre-print
dc.contributor.institutionSchool of Mathematics and Statistics, University College Dublin, Dublin, Ireland
dc.contributor.institutionInsight Centre for Data Analytics, Ireland
dc.identifier.arxivid2107.07561
kaust.personBarreto-Souza, Wagner
kaust.personOmbao, Hernando


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