Simulation-based methods for 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, optimization libraries and graphics processing units for learning complex mappings between data and inferential targets. The resulting tools are amortized, in the sense that, after an initial setup cost, they allow rapid inference through fast feed-forward operations. In this article we review recent progress in the context of point estimation, approximate Bayesian inference, summary-statistic construction, and likelihood approximation. We also cover software, and include a simple illustration to showcase the wide array of tools available for amortized inference and the benefits they offer over 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五十年间随着技术进步取得了显著发展。该领域正在经历一场新的变革，通过利用神经网络的表征能力、优化库和图形处理单元来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，即在支付初始设置成本后，它们能够通过快速前馈操作实现高效推断。本文系统回顾了在点估计、近似贝叶斯推断、摘要统计量构建以及似然函数逼近等领域的最新进展。同时涵盖相关软件工具，并通过一个简明案例展示当前可用于摊销推断的多样化工具集及其相对于马尔可夫链蒙特卡洛方法的优势。文章最后对相关研究主题进行梳理，并对未来研究方向提出展望。