Neural simulation-based inference (SBI) is a popular set of methods for Bayesian inference when models are only available in the form of a simulator. These methods are widely used in the sciences and engineering, where writing down a likelihood can be significantly more challenging than constructing a simulator. However, the performance of neural SBI can suffer when simulators are computationally expensive, thereby limiting the number of simulations that can be performed. In this paper, we propose a novel approach to neural SBI which leverages multilevel Monte Carlo techniques for settings where several simulators of varying cost and fidelity are available. We demonstrate through both theoretical analysis and extensive experiments that our method can significantly enhance the accuracy of SBI methods given a fixed computational budget.

翻译：神经模拟推断（SBI）是一类在模型仅以模拟器形式存在时进行贝叶斯推断的常用方法。这些方法在科学与工程领域被广泛采用，因为在许多情况下，构建模拟器远比显式写出似然函数更为可行。然而，当模拟器计算成本高昂时，神经SBI的性能会受到影响，从而限制了可执行的模拟次数。本文提出一种新颖的神经SBI方法，该方法利用多级蒙特卡罗技术，适用于存在多个具有不同计算成本与保真度的模拟器的场景。通过理论分析与大量实验，我们证明在固定计算预算下，本方法能显著提升SBI方法的准确性。