This monograph provides a rigorous overview of theoretical and methodological aspects of probabilistic inference and learning with Stein's method. Recipes are provided for constructing Stein discrepancies from Stein operators and Stein sets, and properties of these discrepancies such as computability, separation, convergence detection, and convergence control are discussed. Further, the connection between Stein operators and Stein variational gradient descent is set out in detail. The main definitions and results are precisely stated, and references to all proofs are provided.

翻译：本专著系统阐述了基于Stein方法的概率推断与学习的理论与方法学框架。研究提供了从Stein算子与Stein集合构建Stein差异的通用范式，并深入探讨了这些差异的可计算性、分离性、收敛检测与收敛控制等核心性质。此外，本文详细阐述了Stein算子与Stein变分梯度下降之间的理论联系。所有核心定义与定理均以精确的数学语言表述，并附有完整证明的文献指引。