标题： 双变量正态模型的客观先验 显示英文标题

标题： Objective priors for the bivariate normal model

摘要： 研究双变量正态分布引出了涉及客观贝叶斯推断的广泛问题，包括不同类型的目标先验（例如，Jeffreys先验、不变先验、参考先验、匹配先验）、不同的推断模式（例如，贝叶斯推断、频率推断、信仰推断）以及在确定最优目标先验时涉及的标准（例如，计算简便性、频率性质、边际悖论）。针对涉及双变量正态分布的各种推断，给出了关于最优目标先验的总结性建议。在研究过程中，发现了一系列令人惊讶的结果，其中包括存在一些目标先验，它们能为双变量正态参数的许多函数（包括相关系数）提供精确的频率推断。 显示英文摘要

摘要： Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of inference (e.g., Bayesian, frequentist, fiducial) and the criteria involved in deciding on optimal objective priors (e.g., ease of computation, frequentist performance, marginalization paradoxes). Summary recommendations as to optimal objective priors are made for a variety of inferences involving the bivariate normal distribution. In the course of the investigation, a variety of surprising results were found, including the availability of objective priors that yield exact frequentist inferences for many functions of the bivariate normal parameters, including the correlation coefficient.