用模拟器实现贝叶斯推断，提升多变量估计精度
Simulation-Based Empirical Bayes
- 通过模拟器和神经网络逼近隐式似然，实现无需显式密度的贝叶斯估计
- 在多个科学模拟器上验证，相比固定先验的SBI方法，估计误差更低
- 适合需要高精度推断的复杂系统建模，如生物、物理仿真
经验贝叶斯（EB）可对多个相关潜在变量进行联合推断。传统EB假设似然函数p(x|z)可计算，但在许多科学应用中，似然仅可通过模拟器获得。本文提出基于模拟的经验贝叶斯（SBEB），将非参数EB与基于模拟的推断（SBI）结合。SBEB不依赖显式密度，利用观测数据、模拟样本和可复用的推断网络计算EB估计，并迭代优化拟合的EB先验以逼近总体先验。在多个科学模拟器和真实数据集上，结果表明SBEB在估计精度上优于使用固定先验的SBI方法。
原文摘要 · Abstract (English)
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.
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