On some problems of Bayesian region construction with guaranteed coverages

Abstract The general problem of constructing regions that have a guaranteed coverage probability for an arbitrary parameter interest $$\psi \in \Psi $$ ψ ∈ Ψ is considered. developed are Bayesian in nature and the probabilities can be considered as confidences with respect to model obtained by integrating out nuisance parameters using conditional prior given .$$ . Both covering false value (the accuracy) controlled setting sample size. These priori figures merit concerning reliability study while inferences quoted Bayesian. Several problems where obtaining confidence desirable properties proven difficult obtain. For example, it shown approach discussed never leads improper which has issue some regions.