Bayesian Inference for the Beta-Binomial Distribution via Polynomial Expansions

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Journal of Computational and Graphical Statistics, ISSN: 1061-8600, Vol: 11, Issue: 1, Page: 202-207

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Philip J. Everson; Eric T. Bradlow
Informa UK Limited
Mathematics; Decision Sciences; Statistics and Probability
article description
A commonly used paradigm in modeling count data is to assume that individual counts are generated from a Binomial distribution, with probabilities varying between individuals according to a Beta distribution. The marginal distribution of the counts is then BetaBinomial. Bradlow, Hardie, and Fader (2002, p. 189) make use of polynomial expansions to simplify Bayesian computations with Negative-Binomial distributed data. This article exploits similar expansions to facilitate Bayesian inference with data from the Beta-Binomial model. This has great application and computational importance to many problems, as previous research has resorted to computationally intensive numerical integration or Markov chain Monte Carlo techniques.