On a better lower bound for the frequentist probability of coverage of Bayesian credible intervals in restricted parameter spaces

Abstract

For estimating a lower restricted parametric function in the framework of Marchand and Strawderman (2006), we show how $(1-\alpha )\times 100\%$ Bayesian credible intervals can be constructed so that the frequentist probability of coverage is no less than $1-\frac{3\alpha }{2}$. As in Marchand and Strawderman (2013), the findings are achieved through the specification of the spending function of the Bayes credible interval and apply to an “equal-tails” modification of the HPD procedure among others. Our results require a logconcave assumption for the distribution of a pivot, and apply to estimating a lower bounded normal mean with known variance, and to further examples include lower bounded scale parameters from Gamma, Weibull, and Fisher distributions, with the latter also applicable to random effects analysis of variance.