基于模拟的经验贝叶斯

中文摘要 AI 辅助

经验贝叶斯（EB）对许多相关潜在变量进行同时推断。经典EB假设似然p(x | z)是易处理的。然而，在许多科学应用中，似然只能通过模拟器获得。本文针对这种隐式似然开发了EB。我们引入基于模拟的经验贝叶斯（SBEB），它将非参数EB与基于模拟的推断（SBI）联系起来。SBEB通过使用观测数据、模拟器样本和摊销推断网络来计算EB估计，无需显式密度。SBEB迭代地将拟合的EB先验朝着总体先验进行细化。通过几个科学模拟器和真实世界数据，我们证明SBEB比具有固定先验的SBI提高了准确性。

英文摘要

Empirical Bayes (EB) performs simultaneous inference across many related latent variables. Classical EB assumes that the likelihood p(x | z) is tractable. In many scientific applications, however, the likelihood is available only through a simulator. This paper develops EB for such implicit likelihoods. We introduce simulation-based empirical Bayes (SBEB), which connects nonparametric EB to simulation-based inference (SBI). SBEB computes EB estimates without an explicit density by using the observed data, simulator samples, and an amortized inference network. SBEB iteratively refines the fitted EB prior toward the population prior. With several scientific simulators and real-world data, we demonstrate that SBEB improves accuracy over SBI with a fixed prior.

发表机构

• Department of Statistics University of Washington（统计学系华盛顿大学）
• Department of Computer Science Cornell University（计算机科学系康奈尔大学）
• School of Mathematical Sciences and Center for Statistical Science Peking University（数学科学学院与统计科学中心北京大学）
• Departments of Computer Science and Statistics Columbia University（计算机科学与统计学系哥伦比亚大学）

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