Stein operators, kernels and discrepancies for multivariate continuous distributions

Understand

In this paper we present a general framework for Stein's method for multivariate continuous distributions.

• The approach gives a collection of Stein characterisations, among which we highlight score-Stein operators and kernel Stein operators.
• Applications include copulas and distance between posterior distributions.
• We give a general construction for Stein kernels for elliptical distributions and discuss Stein kernels in generality, highlighting connections with Fisher information and mass transport.