Bayesian inference for complex models with an intractable likelihood can be tackled using algorithms performing many calls to computer simulators. These approaches are collectively known as "simulation-based inference" (SBI). Recent SBI methods have made use of neural networks (NN) to provide approximate, yet expressive constructs for the unavailable likelihood function and the posterior distribution. However, they do not generally achieve an optimal trade-off between accuracy and computational demand. In this work, we propose an alternative that provides both approximations to the likelihood and the posterior distribution, using structured mixtures of probability distributions. Our approach produces accurate posterior inference when compared to state-of-the-art NN-based SBI methods, while exhibiting a much smaller computational footprint. We illustrate our results on several benchmark models from the SBI literature.

翻译：对于似然函数难以处理的复杂模型，可通过执行大量计算机仿真调用的算法进行贝叶斯推断，此类方法统称为"仿真推断"（SBI）。现有SBI方法虽利用神经网络（NN）为不可用的似然函数和后验分布提供近似且表达能力强的构造，但通常无法在精度与计算需求间实现最优权衡。本研究提出一种替代方案，采用结构化概率分布混合模型同时逼近似然函数与后验分布。与基于NN的先进SBI方法相比，本方法不仅后验推断精度相当，且计算开销显著降低。我们通过SBI文献中的多个基准模型验证了该方法的有效性。