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