Bayesian Inference for Three Bivariate Beta Binomial Models
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.
Keywords: Bayesian, Bivariate beta binomial, Data augmentation, MCMC, Negative hypergeometric, OpenBUGS, Overdispersion.
Article Information
Article History:
Received Date: 02/06/2017
Revision Received Date: 16/08/2017
Acceptance Date: 22/08/2017
Electronic publication date: 16/10/2017
Collection year: 2017
© 2017 David Peter Michael Scollnik.
open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at:
https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
* Address correspondence to this author at the Department of Mathematics and Statistics, University of, Calgary, 2500 University Drive NW, Calgary, Alberta, Canada, T2N 1N4; Tel: 001-403-220-5210; E-mail: scollnik@ucalgary.ca
Open Peer Review Details |
Manuscript submitted on 02-06-2017 |
Original Manuscript |
Bayesian Inference for Three Bivariate Beta Binomial Models |