On Bayesian credible sets, restricted parameter spaces and frequentist coverage

For estimating a lower bounded parametric function in the framework of Marchand and Strawderman [6], we provide through a unified approach a class of Bayesian confidence intervals with credibility 1 - alpha and frequentist coverage probability bounded below by 1-alpha/1+alpha. In cases where the underlying pivotal distribution is symmetric, the findings represent extensions with respect to the specification of the credible set achieved through the choice of a spending function, and include Marchand and Strawdermans HPD procedure result. For non-symmetric cases, the determination of a such a class of Bayesian credible sets fills a gap in the literature and includes an equal-tails modification of the HPD procedure. Several examples are presented demonstrating wide applicability.