Intrinsic credible regions: An objective Bayesian approach to interval estimation

This paper definesintrinsic credible regions, a method to produce objective Bayesian credible regions which only depends on the assumed model and the available data.Lowest posterior loss (LPL) regions are defined as Bayesian credible regions which contain values of minimum posterior expected loss: they depend both on the loss function and on the prior specification. An invariant, information-theory based loss function, theintrinsic discrepancy is argued to be appropriate for scientific communication. Intrinsic credible regions are the lowest posterior loss regions with respect to the intrinsic discrepancy loss and the appropriate reference prior. The proposed procedure is completely general…