Simulation-Based Empirical Bayes
For scientists using simulators where likelihoods are intractable, SBEB provides a method to perform empirical Bayes inference without explicit densities, improving upon standard simulation-based inference.
This paper introduces simulation-based empirical Bayes (SBEB) for implicit likelihoods where only a simulator is available, connecting nonparametric EB to simulation-based inference. SBEB improves accuracy over SBI with a fixed prior across several scientific simulators and real-world data.
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.