Bayesian Inference for Three Bivariate Beta Binomial Models

David Peter Michael Scollnik ()
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David Peter Michael Scollnik: Department of Mathematics and Statistics, University of Calgary, Calgary, Canada

The Open Statistics and Probability Journal, 2017, vol. 8, issue 1, 27-38

Abstract: Background : This paper considers three two-dimensional beta binomial models previously introduced in the literature. These were proposed as candidate models for modelling forms of correlated and overdispersed bivariate count data. However, the first model has a complicated form of bivariate probability mass function involving a generalized hypergeometric function and the remaining two do not have closed forms of probability mass functions and are not amenable to analysis using maximum likelihood. This limited their applicability. Objective : In this paper, we will discuss how the Bayesian analyses of these models may go forward using Markov chain Monte Carlo and data augmentation. Results : An illustrative example having to do with student achievement in two related university courses is included. Posterior and posterior predictive inferences and predictive information criteria are discussed.

Keywords: Bayesian; Bivariate beta binomial; Data augmentation; MCMC; Negative hypergeometric; OpenBUGS; Overdispersion. (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:ben:tostpj:v:8:y:2017:i:1:p:27-38

DOI: 10.2174/1876527001708010027

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