Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable and empirically rejected. This paper proposes to model the conditional distribution of the parameter given the standard errors as a flexibly parametrized location-scale family of distributions, leading to a family of methods that we call CLOSE. The CLOSE framework unifies and generalizes several proposals under precision dependence. We argue that the most flexible member of the CLOSE family is a minimalist and computationally efficient default for accounting for precision dependence. We analyze this method and show that it is competitive in terms of the regret of subsequent decisions rules. Empirically, using CLOSE leads to sizable gains for selecting high-mobility Census tracts.

翻译：高斯经验贝叶斯方法通常遵循精度独立性假设：感兴趣的未知参数与估计值的已知标准误相互独立。该假设在理论上常受质疑，且在实践中常被拒绝。本文提出将给定标准误时参数的条件分布建模为一个灵活参数化的位置-尺度分布族，由此导出一系列我们称之为CLOSE的方法族。CLOSE框架统一并推广了精度依赖性下的若干现有提案。我们认为CLOSE族中最灵活的成员是处理精度依赖性的一个极简且计算高效的默认选择。我们分析了该方法，并证明其在后续决策规则的遗憾度方面具有竞争力。实证表明，使用CLOSE方法在筛选高流动性人口普查区方面能带来显著增益。