 Highest posterior density interval

A highest posterior density interval is a credible interval whose included points have at least as high posterior density as excluded points, apart from boundary and null-set choices. It is a highest density region of prescribed posterior probability that happens to be an interval. For a continuous unimodal posterior with two interior endpoints, the endpoint densities agree. A monotone posterior on a half-line instead starts at a support boundary, as in a Pareto highest density interval. For a multimodal posterior distribution, the highest-density region can be disconnected and cannot always be represented by a single interval. Density-level regions use a specified parameter coordinate and reference measure; they are not generally preserved by nonlinear reparametrization.