标题： 单峰分布模式的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 As Analogues to Profile Likelihood Ratio Confidence Intervals for Modes of Unimodal Distributions

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特性。 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，它有时因其变换不变性而受到批评。 我们认为HPD区间是频率论置信区间（LRCI）的自然类比。 首先，我们提供有关HPD区间的背景知识，以及似然比检验统计量及其反演以生成渐近正确CIs的方法。 我们的主要结果是证明HPD区间具有与轮廓似然比置信区间（LRCI）类似的优点，例如对于单调函数的模变换不变性。 然后，我们讨论主要结果的应用，一个比较二项式概率参数p的轮廓LRCI与贝叶斯HPD区间用于贝塔分布密度函数的示例情况，两者均用于估计总体比例。 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, it is sometimes criticized for being transformation invariant. We make the case that the HPD interval is a natural analog to the frequentist profile likelihood ratio confidence interval (LRCI). First we provide background on the HPD interval as well as the Likelihood Ratio Test statistic and its inversion to generate asymptotically-correct CIs. Our main result is to show that the HPD interval has similar desirable properties as the profile LRCI, such as transformation invariance with respect to the mode for monotonic functions. We then discuss an application of the main result, an example case which compares the profile LRCI for the binomial probability parameter p with the Bayesian HPD interval for the beta distribution density function, both of which are used to estimate population proportions.