A Riemann–Stein kernel method

Alessandro Barp, Chri S.J. Oates, Emi L.I.O. Porcu, Mark G.I. Rolami

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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.

Original languageBritish English
Pages (from-to)2181-2208
Number of pages28
JournalBernoulli
Volume28
Issue number4
DOIs
StatePublished - Nov 2022

Keywords

  • Bayesian computation
  • kernel Stein discrepancy
  • reproducing kernel
  • Stein equation

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