Bayesian Analysis

Posterior predictive arguments in favor of the Bayes-Laplace prior as the consensus prior for binomial and multinomial parameters

Richard Gerlach, Kerrie Mengersen, and Frank Tuyl

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Abstract

It is argued that the posterior predictive distribution for the binomial and multinomial distributions, when viewed via a hypergeometric-like representation, suggests the uniform prior on the parameters for these models. The argument is supported by studying variations on an example by Fisher, and complements Bayes' original argument for a uniform prior predictive distribution for the binomial. The fact that both arguments lead to invariance under transformation is also discussed.

Article information

Source
Bayesian Anal. Volume 4, Number 1 (2009), 151-158.

Dates
First available in Project Euclid: 22 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1340370393

Digital Object Identifier
doi:10.1214/09-BA405

Mathematical Reviews number (MathSciNet)
MR2486242

Zentralblatt MATH identifier
1330.62156

Keywords
Bayesian inference binomial distribution invariance noninformative priors Jeffreys prior

Citation

Tuyl, Frank; Gerlach, Richard; Mengersen, Kerrie. Posterior predictive arguments in favor of the Bayes-Laplace prior as the consensus prior for binomial and multinomial parameters. Bayesian Anal. 4 (2009), no. 1, 151--158. doi:10.1214/09-BA405. https://projecteuclid.org/euclid.ba/1340370393


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