A note on Bayesian credible sets in restricted parameter space problems and lower bounds for frequentist coverage

For estimating a lower bounded parametric function in the framework of Marchand and Strawderman (2006), we provide "through" a unified approach a class of Bayesian confidence intervals with credibility $1-\alpha$ and frequentist coverage probability bounded below by $\frac{1-\alpha}{1+\alpha}$. 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 {\it spending function}, and including Marchand and Strawderman's HPD procedure result. More significantly for non-symmetric cases, the lower bound $\frac{1-\alpha}{1+\alpha}$ finding, although not applicable to the HPD procedure, is novel. Several examples are presented demonstrating wide applicability.