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Lookup NU author(s): Professor Chris Oates, Professor Emilio Porcu
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© 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.
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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