Simulation-Based Empirical Bayes

Abstract: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.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2607.21843 [stat.ML]

(or arXiv:2607.21843v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2607.21843 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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