We examine the uniqueness of the posterior distribution within an Empirical Bayes framework using a discretized prior. To achieve this, we impose Rational Expectations conditions on the prior, focusing on coherence and stability properties. We derive the conditions necessary for posterior uniqueness when observations are drawn from either discrete or continuous distributions. Additionally, we discuss the properties of our discretized prior as an approximation of the true underlying prior.

翻译：本文在采用离散化先验的经验贝叶斯框架下，研究后验分布的唯一性问题。为实现这一目标，我们对先验施加理性预期条件，重点关注其一致性与稳定性特征。我们推导了当观测值取自离散分布或连续分布时，保证后验唯一性所需的条件。此外，我们还探讨了离散化先验作为真实潜在先验近似所具有的性质。