Mixed neural posterior estimation for simulators with discrete and continuous parameters

TL;DR

This paper extends Neural Posterior Estimation to handle mixed discrete and continuous parameters, enabling accurate inference in complex scientific models with intractable likelihoods.

Contribution

It introduces a joint inference network that combines an autoregressive classifier and a generative model for mixed parameter spaces, with a calibration diagnostic tool.

Findings

Accurate and calibrated posteriors on toy examples and real-world simulators.

Joint inference outperforms methods that ignore parameter space structure.

Framework implemented in the sbi Python package.

Abstract

Neural Posterior Estimation (NPE) enables rapid parameter inference for complex simulators with intractable likelihoods. NPE trains an inference network to estimate a probability density over parameters given data, typically assumed to be \emph{continuous}. However, many scientific models involve parameter spaces that are \emph{mixed}, that is, they contain both discrete and continuous dimensions. We address this limitation by extending NPE to mixed parameter spaces through an inference network that jointly handles discrete and continuous parameters. The inference network factorizes the joint posterior into discrete and continuous components, combining an autoregressive classifier for the discrete parameters with a generative model for the continuous parameters, trained jointly under a single simulation-based objective. In addition, we propose a diagnostic tool to assess the calibration of the mixed posterior approximation. Across tractable toy examples and real-world scientific simulators, our joint inference approach yields accurate and calibrated posteriors. The inference framework is available in the \texttt{sbi} Python package.