In recent years, empirical Bayesian (EB) inference has become an attractive approach for estimation in parametric models arising in a variety of real-life problems, especially in complex and high-dimensional scientific applications. However, compared to the relative abundance of available general methods for computing point estimators in the EB framework, the construction of confidence sets and hypothesis tests with good theoretical properties remains difficult and problem specific. Motivated by the universal inference framework of Wasserman et al. (2020), we propose a general and universal method, based on holdout likelihood ratios, and utilizing the hierarchical structure of the specified Bayesian model for constructing confidence sets and hypothesis tests that are finite sample valid. We illustrate our method through a range of numerical studies and real data applications, which demonstrate that the approach is able to generate useful and meaningful inferential statements in the relevant contexts.

翻译：近年来，经验贝叶斯推断已成为参数模型中一种富有吸引力的估计方法，这些模型广泛应用于各类实际问题，尤其在复杂高维科学应用中表现突出。然而，尽管在经验贝叶斯框架下已有相对丰富的点估计通用计算方法，但具有良好理论性质的置信集构建与假设检验仍面临困难且具有问题特异性。受Wasserman等人(2020)通用推断框架启发，本文提出一种基于留出似然比、利用指定贝叶斯模型层次结构的通用方法，用于构建有限样本有效的置信集与假设检验。通过一系列数值研究与真实数据应用，我们验证了该方法能够在相关情境中生成有用且具实质意义的推断结论。