🤖 AI Summary
Existing neural posterior estimation methods struggle to handle mixed parameter spaces containing both discrete and continuous variables, limiting their applicability in complex scientific simulations. This work presents the first extension of simulation-based inference (SBI) to such hybrid spaces by introducing a unified joint inference framework: it models discrete parameters via an autoregressive classifier and continuous parameters through a generative model, with both components trained jointly under a single objective. Implemented within the sbi toolkit and accompanied by posterior calibration diagnostics, the proposed method yields accurate and well-calibrated posterior estimates across multiple analytically tractable toy models and realistic scientific simulators, substantially enhancing the practicality and reliability of inference in mixed-parameter settings.
📝 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.