Slice sampling on Riemannian manifolds

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.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Passau

Year

2025

Author dc:creator

• Hasenpflug, Mareike

Contributors dc:contributor

• Rudolf, Daniel
• Douc, Randal

• Markov chain Monte Carlo
• Slice sampling
• Riemannian manifolds

Statement dc:rights

• Creative Commons - CC BY - Namensnennung 4.0 International

Repository record source_url

https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/1590

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-passau:1590