ABSTRACT
The reference prior is based on the amount of entropy information measure on the parameter of interest, that an experiment is expected to provide, and on the missing information about the parameter, as a function of the prior p{9). The reference prior is then the one that maximizes the missing information functional. It is obtained usually via a limiting process, by applying Bayes theorem to the posterior (Bernardo and Smith, 1994, page 306). Under some regu larity conditions, the reference prior can be characterized in terms of the parametric model, and it agrees with Jeffrey’s prior, both being proportional to the square root of Fisher’s information. This leads to beta( 1/2,1/2) for Bernoulli sampling, and beta(0,1/2) for Pas cal sampling. The Reference prior can be shown to be independent of the sample size, invariant under one-to-one transformation, and is compatible with sufficient statistics (Bernardo and Smith, 1994, page 309).
