Robust Neural Posterior Estimation and Statistical Model Criticism
This work addresses the challenge of robust inference for scientists using simulators with imperfect models, though it is incremental as it builds on existing neural posterior estimation methods.
The paper tackles the problem of unreliable parameter inference in simulation models when there is a mismatch between the simulator and real data (model misspecification), proposing Robust Neural Posterior Estimation (RNPE) to address this by modeling discrepancies, and finds that RNPE performs well on misspecified tasks while naive methods fail.
Computer simulations have proven a valuable tool for understanding complex phenomena across the sciences. However, the utility of simulators for modelling and forecasting purposes is often restricted by low data quality, as well as practical limits to model fidelity. In order to circumvent these difficulties, we argue that modellers must treat simulators as idealistic representations of the true data generating process, and consequently should thoughtfully consider the risk of model misspecification. In this work we revisit neural posterior estimation (NPE), a class of algorithms that enable black-box parameter inference in simulation models, and consider the implication of a simulation-to-reality gap. While recent works have demonstrated reliable performance of these methods, the analyses have been performed using synthetic data generated by the simulator model itself, and have therefore only addressed the well-specified case. In this paper, we find that the presence of misspecification, in contrast, leads to unreliable inference when NPE is used naively. As a remedy we argue that principled scientific inquiry with simulators should incorporate a model criticism component, to facilitate interpretable identification of misspecification and a robust inference component, to fit 'wrong but useful' models. We propose robust neural posterior estimation (RNPE), an extension of NPE to simultaneously achieve both these aims, through explicitly modelling the discrepancies between simulations and the observed data. We assess the approach on a range of artificially misspecified examples, and find RNPE performs well across the tasks, whereas naively using NPE leads to misleading and erratic posteriors.