SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 1, Page 229-260, January 2020.
The goal of this paper is to explore the basic approximate Bayesian computation (ABC) algorithm via the lens of information theory. ABC is a widely used algorithm in cases where the likelihood of the data is hard to work with or intractable, but one can simulate from it. We use relative entropy ideas to analyze the behavior of the algorithm as a function of the threshold parameter and of the size of the data. Relative entropy here is data driven, as it depends on the values of the observed statistics. Relative entropy also allows us to explore the effect of the distance metric and sets up a mathematical framework for sensitivity analysis allowing us to find important directions which could lead to lower computational cost of the algorithm for the same level of accuracy. In addition, we also investigate the bias of the estimators for generic observables as a function of both the threshold parameters and the size of the data. Our analysis provides error bounds on performance for positive tolerances and finite sample sizes. Simulation studies complement and illustrate the theoretical results.

中文翻译：

---

近似贝叶斯计算的信息几何

SIAM / ASA不确定性量化期刊，第8卷，第1期，第229-260页，2020年1月。
本文的目的是通过信息论的视角探索基本的近似贝叶斯计算（ABC）算法。ABC是一种广泛使用的算法，可用于难以处理或难以处理的数据可能性，但可以从中进行模拟的情况。我们使用相对熵的思想来分析算法的行为，作为阈值参数和数据大小的函数。这里的相对熵是数据驱动的，因为它取决于观察到的统计数据的值。相对熵还使我们能够探索距离度量的效果，并建立了灵敏度分析的数学框架，从而使我们能够找到重要的方向，从而可以在相同精度水平下降低算法的计算成本。此外，我们还研究了阈值参数和数据大小的函数，针对通用可观测量的估计量偏差。我们的分析为正公差和有限的样本量提供了性能上的误差界限。仿真研究补充并说明了理论结果。