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, the trade-off between accuracy and computational demand leaves much space for improvement. 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, even for multimodal posteriors, while exhibiting a much smaller computational footprint. We illustrate our results on several benchmark models from the SBI literature and on a biological model of the translation kinetics after mRNA transfection.

翻译：对于似然函数难以处理的复杂模型，可通过多次调用计算机仿真器进行贝叶斯推断。这类方法统称为"基于仿真的推断"。近期SBI方法利用神经网络为不可得的似然函数和后验分布提供了近似但富有表达力的构造。然而，精度与计算需求之间的权衡仍有很大改进空间。本研究提出一种替代方案，通过结构化概率分布混合同时逼近似然函数和后验分布。与基于神经网络的最先进SBI方法相比，即使面对多峰后验分布，本方法仍能提供准确的后验推断，同时计算开销显著降低。我们在SBI文献中的多个基准模型以及mRNA转染后翻译动力学的生物模型上验证了本方法的有效性。