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：对于具有难以计算的似然函数的复杂模型，贝叶斯推断可通过调用计算机模拟器多次的算法来实现。这类方法统称为“基于仿真的推断”（SBI）。近年来的SBI方法利用神经网络（NN）为未知的似然函数和后验分布提供近似但具有表达力的构造。然而，这些方法通常无法在精度与计算需求之间实现最优权衡。本研究提出了一种替代方案，该方法利用概率分布的结构化混合，同时为似然函数和后验分布提供近似。与基于NN的顶尖SBI方法相比，本方法在实现准确后验推断的同时，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所提方法的效果。