Optimal properties of some Bayesian inferences

Details Optimal properties of some Bayesian inferences Optimal properties of some Bayesian inferences

2007-10-05

arxiv.org/abs/0710.1151v2

Electronic Journal of Statistics 2008, Vol. 2, 1268-1280

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-EJS126 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

10.1214/07-EJS126

Relative surprise regions are shown to minimize, among Bayesian credible regions, the prior probability of covering a false value from the prior. Such regions are also shown to be unbiased in the sense that the prior probability of covering a false value is bounded above by the prior probability of covering the true value. Relative surprise regions are shown to maximize both the Bayes factor in favor of the region containing the true value and the relative belief ratio, among all credible regions with the same posterior content. Relative surprise regions emerge naturally when we consider equivalence classes of credible regions generated via reparameterizations.

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