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A Riemann–Stein kernel method

Lookup NU author(s): Professor Chris OatesORCiD, Professor Emilio Porcu

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Abstract

© 2022 ISI/BS.This paper proposes and studies a numerical method for approximation of posterior expectations based on interpolation with a Stein reproducing kernel. Finite-sample-size bounds on the approximation error are established for posterior distributions supported on a compact Riemannian manifold, and we relate these to a kernel Stein discrepancy (KSD). Moreover, we prove in our setting that the KSD is equivalent to Sobolev discrepancy and, in doing so, we completely characterise the convergence-determining properties of KSD. Our contribution is rooted in a novel combination of Stein’s method, the theory of reproducing kernels, and existence and regularity results for partial differential equations on a Riemannian manifold.

Publication metadata

Author(s): Barp A, Oates CSJ, Porcu ELIO, Rolami MGI

Publication type: Article

Publication status: Published

Journal: Bernoulli

Year: 2022

Volume: 28

Issue: 4

Pages: 2181-2208

Print publication date: 01/11/2022

Online publication date: 01/11/2022

Acceptance date: 02/04/2018

Publisher: Bernoulli Society for Mathematical Statistics and Probability

URL: https://doi.org/10.3150/21-BEJ1415

DOI: 10.3150/21-BEJ1415

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