Conservative neural posterior estimation via distributionally robust training

Simulation-based inference with neural posterior estimation (NPE) often yields overconfident and unreliable posteriors under limited simulation budgets. To address this, we propose DRO-NPE, a distributionally robust approach that replaces the standard NPE objective with a worst-case loss over a Wasserstein ambiguity set. We introduce KL-based metrics for miscoverage and miscalibration, and use these to show that the DRO-NPE objective controls overfitting and reduces posterior overconfidence. Our method is tractable, parallelisable, and readily integrates with standard normalising flows. Across benchmark SBI tasks, DRO-NPE consistently improves coverage and calibration, while narrowing the gap between empirical and population NPE loss, leading to more reliable inference in low-simulation regimes.

Amortised and provably-robust simulation-based inference

Complex simulator-based models are now routinely used to perform inference across the sciences and engineering, but existing inference methods are often unable to account for outliers and other extreme values in data which occur due to faulty measurement instruments or human error. In this paper, we introduce a novel approach to simulation-based inference grounded in generalised Bayesian inference and a neural approximation of a weighted score-matching loss. This leads to a method that is both amortised and provably robust to outliers, a combination not achieved by existing approaches. Furthermore, through a carefully chosen conditional density model, we demonstrate that inference can be further simplified and performed without the need for Markov chain Monte Carlo sampling, thereby offering significant computational advantages, with complexity that is only a small fraction of that of current state-of-the-art approaches.

Multilevel neural simulation-based inference

Neural simulation-based inference (SBI) is a popular set of methods for Bayesian inference when models are only available in the form of a simulator. These methods are widely used in the sciences and engineering, where writing down a likelihood can be significantly more challenging than constructing a simulator. However, the performance of neural SBI can suffer when simulators are computationally expensive, thereby limiting the number of simulations that can be performed. In this paper, we propose a novel approach to neural SBI which leverages multilevel Monte Carlo techniques for settings where several simulators of varying cost and fidelity are available. We demonstrate through both theoretical analysis and extensive experiments that our method can significantly enhance the accuracy of SBI methods given a fixed computational budget.