Simulation-based methods for making statistical inference have evolved dramatically over the past 50 years, keeping pace with technological advancements. The field is undergoing a new revolution as it embraces the representational capacity of neural networks, optimisation libraries, and graphics processing units for learning complex mappings between data and inferential targets. The resulting tools are amortised, in the sense that they allow inference to be made quickly through fast feedforward operations. In this article we review recent progress made in the context of point estimation, approximate Bayesian inference, the automatic construction of summary statistics, and likelihood approximation. The review also covers available software, and includes a simple illustration to showcase the wide array of tools available for amortised inference and the benefits they offer over state-of-the-art Markov chain Monte Carlo methods. The article concludes with an overview of relevant topics and an outlook on future research directions.

翻译：基于仿真的统计推断方法在过去50年间随着技术进步发生了巨大变革。当前该领域正经历一场全新革命：利用神经网络的表征能力、优化库以及图形处理器，学习数据与推断目标之间的复杂映射关系。由此产生的工具具有摊销特性，即通过快速前馈运算实现高效推断。本文回顾了点估计、近似贝叶斯推断、汇总统计量自动构建及似然函数近似等领域的最新进展。综述同时涵盖现有软件工具，并通过简单实例展示摊销推断工具集的多样性及其相较于先进马尔可夫链蒙特卡洛方法的优势。最后总结相关研究主题，展望未来发展方向。