{"id":{"repo_id":"passau-thes","oai_identifier":"oai:kobv.de-opus4-uni-passau:1590"},"canonical_url":"https://search.dev.ndltd.org/etd/passau-thes/oai:kobv.de-opus4-uni-passau:1590","repository":{"repo_id":"passau-thes","name":"Universität Passau","base_url":"https://opus4.kobv.de/opus4-uni-passau/oai"},"display":{"title":"Slice sampling on Riemannian manifolds","abstract":"This thesis is concerned with hybrid slice samplers for approximate sampling of distributions on Riemannian manifolds. First for distributions on the Euclidean unit sphere, and then for distributions on general Riemannian manifolds we introduce a geodesic-based hybrid slice sampler, called geodesic slice sampler. Under mild regularity assumptions, we establish reversibility with respect to the target distribution for this sampler and positive semi-definiteness of the corresponding operator. Moreover, on compact Riemannian manifolds we show uniform ergodicity with explicit constants for the geodesic slice sampler if the target distribution has a bounded density with respect to the Riemannian measure. As an important building block of this sampler, we provide an explicit expression for the shrinkage procedure proposed in (Neal, 2003) in terms of a Markov kernel. We establish that this kernel is reversible with respect to the uniform distribution on the target set and that its corresponding operator is positive semi-definite. Beyond the geodesic slice sampler, we apply these results also to elliptical slice sampling (Murray, Adams, MacKay, 2010) to obtain a proof for its reversibility with respect to the target distribution and positive semi-definiteness of the corresponding operator.","abstract_html":"This thesis is concerned with hybrid slice samplers for approximate sampling of distributions on Riemannian manifolds. First for distributions on the Euclidean unit sphere, and then for distributions on general Riemannian manifolds we introduce a geodesic-based hybrid slice sampler, called geodesic slice sampler. Under mild regularity assumptions, we establish reversibility with respect to the target distribution for this sampler and positive semi-definiteness of the corresponding operator. Moreover, on compact Riemannian manifolds we show uniform ergodicity with explicit constants for the geodesic slice sampler if the target distribution has a bounded density with respect to the Riemannian measure. As an important building block of this sampler, we provide an explicit expression for the shrinkage procedure proposed in (Neal, 2003) in terms of a Markov kernel. We establish that this kernel is reversible with respect to the uniform distribution on the target set and that its corresponding operator is positive semi-definite. Beyond the geodesic slice sampler, we apply these results also to elliptical slice sampling (Murray, Adams, MacKay, 2010) to obtain a proof for its reversibility with respect to the target distribution and positive semi-definiteness of the corresponding operator.","abstract_has_math":false,"creators":["Hasenpflug, Mareike"],"institution":"Universität Passau","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Rudolf, Daniel","Douc, Randal"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-05-07","date_published":"2025-05-07","updated_at":"2026-07-24T03:45:10Z","subjects":["Markov chain Monte Carlo","Slice sampling","Riemannian manifolds"],"languages":[],"rights":["Creative Commons - CC BY - Namensnennung 4.0 International"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/1590","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rudolf, Daniel","Douc, Randal"]},{"key":"dc:creator","label":"Author","values":["Hasenpflug, Mareike"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universität Passau"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Passau"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Markov chain Monte Carlo","Slice sampling","Riemannian manifolds"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Creative Commons - CC BY - Namensnennung 4.0 International"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis is concerned with hybrid slice samplers for approximate sampling of distributions on Riemannian manifolds. First for distributions on the Euclidean unit sphere, and then for distributions on general Riemannian manifolds we introduce a geodesic-based hybrid slice sampler, called geodesic slice sampler. Under mild regularity assumptions, we establish reversibility with respect to the target distribution for this sampler and positive semi-definiteness of the corresponding operator. Moreover, on compact Riemannian manifolds we show uniform ergodicity with explicit constants for the geodesic slice sampler if the target distribution has a bounded density with respect to the Riemannian measure. As an important building block of this sampler, we provide an explicit expression for the shrinkage procedure proposed in (Neal, 2003) in terms of a Markov kernel. We establish that this kernel is reversible with respect to the uniform distribution on the target set and that its corresponding operator is positive semi-definite. Beyond the geodesic slice sampler, we apply these results also to elliptical slice sampling (Murray, Adams, MacKay, 2010) to obtain a proof for its reversibility with respect to the target distribution and positive semi-definiteness of the corresponding operator."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Slice sampling on Riemannian manifolds"]}]}],"canonical_facts":{"dc:contributor":["Rudolf, Daniel","Douc, Randal"],"dc:creator":["Hasenpflug, Mareike"],"dc:description.abstract":["This thesis is concerned with hybrid slice samplers for approximate sampling of distributions on Riemannian manifolds. First for distributions on the Euclidean unit sphere, and then for distributions on general Riemannian manifolds we introduce a geodesic-based hybrid slice sampler, called geodesic slice sampler. Under mild regularity assumptions, we establish reversibility with respect to the target distribution for this sampler and positive semi-definiteness of the corresponding operator. Moreover, on compact Riemannian manifolds we show uniform ergodicity with explicit constants for the geodesic slice sampler if the target distribution has a bounded density with respect to the Riemannian measure. As an important building block of this sampler, we provide an explicit expression for the shrinkage procedure proposed in (Neal, 2003) in terms of a Markov kernel. We establish that this kernel is reversible with respect to the uniform distribution on the target set and that its corresponding operator is positive semi-definite. Beyond the geodesic slice sampler, we apply these results also to elliptical slice sampling (Murray, Adams, MacKay, 2010) to obtain a proof for its reversibility with respect to the target distribution and positive semi-definiteness of the corresponding operator."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universität Passau"],"dc:rights":["Creative Commons - CC BY - Namensnennung 4.0 International"],"dc:subject":["Markov chain Monte Carlo","Slice sampling","Riemannian manifolds"],"dc:title":["Slice sampling on Riemannian manifolds"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Passau"]},"updated_at":"2026-07-24T03:45:10Z"}