发表机构
Faculty of Economics, Keio University; Department of Statistics, Operations, and Data Science, Temple University（庆应义塾大学经济学部; 天普大学统计、运营与数据科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出条件f建模框架，利用条件边际得分函数直接估计后验量，避免显式先验建模，通过能量表示和得分匹配处理协变量效应，模拟和RNA-seq实验验证了其有效性。
AI 中文摘要
我们提出了条件f建模（Cf-modeling），这是一个带有协变量的经验贝叶斯推断框架。一个核心恒等式表明，条件边际得分函数不仅通过Tweedie公式决定后验均值，还决定后验矩生成函数，为无需显式先验建模即可恢复后验量提供了基础。受此观察启发，我们将条件边际得分视为推断的主要对象，并使用基于能量的表示和Hyvärinen得分匹配直接估计它，从而避免了可能难以处理的协变量依赖归一化常数。所提出的框架灵活地适应协变量效应和异方差性，并为后验矩估计和不确定性量化提供了实用方法。我们通过模拟和一个RNA-seq应用证明了所提出方法的有效性。
英文摘要
We propose conditional f-modeling (Cf-modeling), a framework for empirical Bayes inference with covariates. A central identity shows that the conditional marginal score function determines not only the posterior mean through Tweedie's formula, but also the posterior moment-generating function, providing a basis for recovering posterior quantities without explicit prior modeling. Motivated by this observation, we treat the conditional marginal score as the primary object of inference and estimate it directly using an energy-based representation and Hyvärinen score matching, thereby avoiding potentially intractable covariate-dependent normalizing constants. The resulting framework flexibly accommodates covariate effects and heteroscedasticity and provides a practical approach to posterior moment estimation and uncertainty quantification. We demonstrate the effectiveness of the proposed method through simulations and an RNA-seq application.
Comments28 pages (main) + 6 pages (supplement)
