{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,17]],"date-time":"2026-10-17T17:10:00Z","timestamp":1792257000532,"version":"4.4.0"},"reference-count":42,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Union","doi-asserted-by":"publisher","award":["ERC-2022-SYG-OCEAN-101071601"],"award-info":[{"award-number":["ERC-2022-SYG-OCEAN-101071601"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,2,13]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>We propose a theoretically justified and practically applicable slice-sampling-based Markov chain Monte Carlo method for approximate sampling from probability measures on Riemannian manifolds. The latter naturally arise as posterior distributions in Bayesian inference of matrix-valued parameters, for example belonging to either the Stiefel or the Grassmann manifold. Our method, called geodesic slice sampling, generalizes hit-and-run slice sampling on $ \\mathbb{R}^{d} $ to Riemannian manifolds by abstracting straight lines to geodesics. It is reversible with respect to the distribution of interest and converges to the latter in total variation distance. We demonstrate the robustness of our sampler\u2019s performance compared to other Markov chain Monte Carlo methods dealing with manifold-valued distributions through extensive numerical experiments, on both synthetic and real data. In particular, we illustrate the sampler\u2019s remarkable ability to cope with anisotropic target densities, without using gradient information and preconditioning.<\/jats:p>","DOI":"10.1093\/biomet\/asag006","type":"journal-article","created":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T12:08:06Z","timestamp":1769515686000},"source":"Crossref","is-referenced-by-count":1,"title":["Geodesic slice sampling on Riemannian manifolds"],"prefix":"10.1093","volume":"113","author":[{"given":"Alain","family":"Durmus","sequence":"first","affiliation":[{"name":"Center for Applied Mathematics, \u00c9cole Polytechnique , 91128 Palaiseau Cedex,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Samuel","family":"Gruffaz","sequence":"additional","affiliation":[{"name":"Centre Borelli, Universit\u00e9 Paris Saclay , 4 avenue des Sciences , 91190 Gif-sur-Yvette,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mareike","family":"Hasenpflug","sequence":"additional","affiliation":[{"name":"Center for Applied Mathematics, \u00c9cole Polytechnique , 91128 Palaiseau Cedex,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel","family":"Rudolf","sequence":"additional","affiliation":[{"name":"Faculty for Computer Science and Mathematics, University of Passau , Innstra\u00dfe 33 , 94032 Passau,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,2,6]]},"reference":[{"key":"2026060915361052600_asag006-B1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-7643-7480-8","volume-title":"Analysis III","author":"Amann","year":"2009"},{"key":"2026060915361052600_asag006-B2","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1109\/TMI.2003.822821","article-title":"Probabilistic independent component analysis for functional magnetic resonance imaging","volume":"23","author":"Beckmann","year":"2004","journal-title":"IEEE Trans. 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