Bayesian Interval Estimates Which are Also Confidence Intervals

SUMMARY Let Y 1, . . ., Yn denote independent observations each distributed according to a distribution depending on a scalar parameter θ suppose that we are interested in constructing an interval estimate for θ. One approach is to use Bayesian inference. For a given prior density, we can construct an interval such that the posterior probability that θ lies in the interval is some specified value. In this paper, a method is given for constructing a Bayesian interval estimate such that the coverage probability of the interval is approximately equal to the posterior probability of the interval.