标题： 关于受限参数空间问题中的贝叶斯可信集和频率覆盖的下界 显示英文标题

标题： On Bayesian credible sets in restricted parameter space problems and lower bounds for frequentist coverage

摘要： 在 Marchand 和 Strawderman (2006) 提出的框架下估计一个下有界的参数函数时，我们通过一种统一的方法提供了一类置信度为$1-\alpha$的贝叶斯置信区间，其频率覆盖概率被下界限制为$\frac{1-\alpha}{1+\alpha}$。 在潜在枢轴分布是对称的情况下，这些结果相对于通过选择{\it 支出函数}来指定可信集有所扩展，并包含了 Marchand 和 Strawderman 的最高后验密度（HPD）程序的结果。 对于非对称情况，确定这样一类贝叶斯可信集填补了文献中的空白，并包括了对 HPD 程序的一种“等尾”修改。 给出了多个例子以展示其广泛适用性。 显示英文摘要

摘要： For estimating a lower bounded parametric function in the framework of Marchand and Strawderman (2006), we provide through a unified approach a class of Bayesian confidence intervals with credibility $1-\alpha$ and frequentist coverage probability bounded below by $\frac{1-\alpha}{1+\alpha}$. In cases where the underlying pivotal distribution is symmetric, the findings represent extensions with respect to the specification of the credible set achieved through the choice of a {\it spending function}, and include Marchand and Strawderman's HPD procedure result. For non-symmetric cases, the determination of a such a class of Bayesian credible sets fills a gap in the literature and includes an "equal-tails" modification of the HPD procedure. Several examples are presented demonstrating wide applicability.