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Bayesian Inference for Three Bivariate Beta Binomial Models

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  • David Peter Michael Scollnik

    (Department of Mathematics and Statistics, University of Calgary, Calgary, Canada)

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.

Suggested Citation

  • David Peter Michael Scollnik, 2017. "Bayesian Inference for Three Bivariate Beta Binomial Models," The Open Statistics and Probability Journal, Bentham Open, vol. 8(1), pages 27-38, October.
    • Handle: RePEc:ben:tostpj:v:8:y:2017:i:1:p:27-38
    DOI: 10.2174/1876527001708010027
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    References listed on IDEAS

    as
    1. Danaher, Peter J. & Hardie, Bruce G.S., 2005. "Bacon With Your Eggs? Applications of a New Bivariate Beta-Binomial Distribution," The American Statistician, American Statistical Association, vol. 59, pages 282-286, November.
    2. Goro Ishii & Reiko Hayakawa, 1960. "On the compound binomial distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 12(1), pages 69-80, February.
    3. Bibby, Bo Martin & Væth, Michael, 2011. "The two-dimensional beta binomial distribution," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 884-891, July.
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