Preconditioned Robust Neural Posterior Estimation for Misspecified Simulators

TL;DR

This paper introduces a preconditioning method for neural posterior estimation in simulation-based inference that improves robustness and accuracy under model misspecification by focusing training on relevant data regions.

Contribution

It proposes a novel preconditioning approach that enhances neural posterior estimation robustness in misspecified models, including a forest-proximity preconditioning technique.

Findings

Preconditioning improves stability and accuracy of neural posterior estimation.

The method enhances calibration and posterior-predictive fit.

Demonstrated effectiveness on synthetic and real examples.

Abstract

Simulation-based inference (SBI) enables parameter estimation for complex stochastic models with intractable likelihoods when model simulation is feasible. Neural posterior estimation (NPE) is a popular SBI approach that often achieves accurate inference with far fewer simulations than classical approaches. But in practice, neural approaches can be unreliable for two reasons: incompatible data summaries arising from model misspecification yield unreliable posteriors due to extrapolation, and prior-predictive draws can produce extreme summaries that lead to difficulties in obtaining an accurate posterior for the observed data of interest. Existing preconditioning schemes target well-specified settings, and their behaviour under misspecification remains unexplored. We study preconditioning under misspecification and propose preconditioned robust neural posterior estimation, which computes data-dependent weights that focus training near the observed summaries and fits a robust neural posterior approximation. We also introduce a forest-proximity preconditioning approach that uses tree-based proximity scores to down-weight outlying simulations and concentrate computation around the observed dataset. Across two synthetic examples and one real example with incompatible summaries and extreme prior-predictive behaviour, we demonstrate that preconditioning combined with robust NPE increases stability and improves accuracy, calibration, and posterior-predictive fit over standard baseline methods.