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.
Neural simulation-based inference enables parameter estimation for complex models, but typically requires the user to specify a simulator encoding a fixed model structure. We present a framework for joint model selection and parameter estimation that combines large language model…
Simulation-based inference (SBI) with machine learning is an increasingly important tool for solving inverse problems in science and engineering, including parameter inference and the inversion of detector effects. We provide an overview of the Bayesian and frequentist statistica…
Empirical Bayes (EB) estimators can match the first-order asymptotic risk of maximum likelihood (ML) while behaving very differently at second order: recent excess mean squared error (XMSE) analysis shows that kernel-based EB estimation may be worse than ML when the kernel is poo…
Longitudinal tumor measurements, dropout information, and genetic covariates provide complementary information about treatment response, but integrating these data sources within a single population modeling framework remains challenging. We extend the empirical Bayes variational…
Linear Independent Component Analysis (ICA) recovers jointly independent source signals from their linear mixtures. To achieve this, classical ICA algorithms attempt to maximize non-Gaussianity, measured by negentropy, which is linked to independence by information theory. Becaus…
Sepsis is a leading cause of mortality, yet optimal treatment policies remain contested. Existing reinforcement learning (RL) approaches learn fixed strategies for sepsis treatment, limiting adaptability to changing clinical objectives during inference. We propose EHRMPC, a frame…