标题： 单峰分布的最高后验密度区间作为轮廓似然比置信区间的类比 显示英文标题

标题： Highest Posterior Density Intervals of Unimodal Distributions As Analogues to Profile Likelihood Ratio Confidence Intervals

摘要： 在贝叶斯统计中，最高后验密度（HPD）区间常用于描述后验分布的性质。 作为一种估计置信区间（CIs）的方法，HPD具有两个主要的优点。 首先，它是具有指定覆盖概率的最短区间。 其次，HPD区间内的每一个点的密度都大于区间外每一个点的密度。 然而，HPD区间有时因其变换不变性而受到批评。 我们认为，在某些条件下，HPD区间是频率论似然比置信区间（LRCI）的一个自然类比。 我们的主要结果是推导一个证明，表明在指定条件下，相对于密度峰值的HPD区间对于单调函数具有变换不变性，这种特性与似然比置信区间类似。 显示英文摘要

摘要： In Bayesian statistics, the highest posterior density (HPD) interval is often used to describe properties of a posterior distribution. As a method for estimating confidence intervals (CIs), the HPD has two main desirable properties. Firstly, it is the shortest interval to have a specified coverage probability. Secondly, every point inside the HPD interval has a density greater than every point outside the interval. However, the HPD interval is sometimes criticized for being transformation invariant. We make the case that under certain conditions the HPD interval is a natural analog to the frequentist profile likelihood ratio confidence interval (LRCI). Our main result is to derive a proof showing that under specified conditions, the HPD interval with respect to the density mode is transformation invariant for monotonic functions in a manner which is similar to a profile LRCI.