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.

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