- Title
- Consensus priors in the presence of general laws
- Creator
- Tuyl, Frank; Gerlach, Richard; Mengersen, Kerrie
- Relation
- Journal of Applied Probability & Statistics Vol. 5, Issue 1, p. 31-42
- Relation
- http://japs.isoss.net/may10.htm
- Publisher
- Dixie W Publishing
- Resource Type
- journal article
- Date
- 2010
- Description
- In the context of Bayesian estimation of models for binary data, with parameter θ representing the true proportion of successes, Jeffreys studied the possibility of putting a prior point probability mass on the extremes to allow for general laws θ = 0 or θ = 1. Bernardo’s apparent improvement, based on the choice between homogeneity and heterogeneity, reflects a bias towards the proposed general law after the first observation, which seems unjustified: a success or failure has to occur. A straightforward adjustment considering the situation after the first observation, for both the hypergeometric and binomial models, is proposed for a consensus prior, i.e. a generally agreed on noninformative prior. This recommendation generalises under the multinomial model, for which a new rule, catering for many potential general laws, is proposed. Finally, the inconsistency between the uniform prior for the hypergeometric parameter and the U-shaped reference/Jeffreys prior for the binomial parameter is also discussed.
- Subject
- hypergeometric; binomial; multinomial; Bayes-Laplace prior; Jeffreys prior; reference prior; point probability mass
- Identifier
- http://hdl.handle.net/1959.13/931880
- Identifier
- uon:11194
- Identifier
- ISSN:1930-6792
- Language
- eng
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