arXiv subjects

Mareike Hasenpflug

Publications and source records attributed to Mareike Hasenpflug.

5 recordsLinked to original sources

arXiv2026

Geodesic slice sampling on the sphere

Probability measures on the sphere form an important class of statistical models and are used, for example, in modeling directional data or shapes. Due to their widespread use, but also as an algorithmic building block, efficient sampling of distributions on the sphere is highly desirable. We propose a shrinkage based and an idealized geodesic slice sampling Markov chain, designed to generate approximate samples from distributions on the sphere. In particular, the shrinkage-based version of the algorithm can be implemented such that it runs efficiently and has no tuning parameters. We verify reversibility and prove that under weak regularity conditions geodesic slice sampling is uniformly ergodic. Numerical experiments show that the proposed slice samplers achieve excellent mixing on challenging targets including distributions arising in rigid-registration problems and mixtures of von Mises-Fisher distributions. In these settings our approach outperforms standard samplers such as random-walk Metropolis-Hastings and Hamiltonian Monte Carlo.

stat.ME↗

arXiv2025

Uniform ergodicity of geodesic slice sampling

Geodesic slice sampling, introduced in Durmus et al., 2024, is a slice sampling based Markov chain Monte Carlo method for approximate sampling from distributions on Riemannian manifolds. We prove that it is uniformly ergodic for distributions with compact support that have a bounded density with respect to the Riemannian measure. The constants in our convergence bound are available explicitly, and we investigate their dependence on the hyperparameters of the geodesic slice sampler, the target distribution and the underlying domain.

math.ST↗

arXiv2025

Geodesic slice sampling on Riemannian manifolds

We propose a theoretically justified and practically applicable slice sampling based Markov chain Monte Carlo (MCMC) 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, is reversible with respect to the distribution of interest, and generalizes Hit-and-run slice sampling on $\mathbb{R}^{d}$ to Riemannian manifolds by using geodesics instead of straight lines. We demonstrate the robustness of our sampler's performance compared to other MCMC methods dealing with manifold valued distributions through extensive numerical experiments, on both synthetic and real data. In particular, we illustrate its remarkable ability to cope with anisotropic target densities, without using gradient information and preconditioning.

stat.CO↗

arXiv2024

Reversibility of elliptical slice sampling revisited

We extend elliptical slice sampling, a Markov chain transition kernel suggested in Murray, Adams and MacKay 2010, to infinite-dimensional separable Hilbert spaces and discuss its well-definedness. We point to a regularity requirement, provide an alternative proof of the desirable reversibility property and show that it induces a positive semi-definite Markov operator. Crucial within the proof of the formerly mentioned results is the analysis of a shrinkage Markov chain that may be interesting on its own.

math.ST↗

arXiv2023

Wasserstein convergence rates of increasingly concentrating probability measures

For $\ell\colon \mathbb{R}^d \to [0,\infty)$ we consider the sequence of probability measures $\left(μ_n\right)_{n \in \mathbb{N}}$, where $μ_n$ is determined by a density that is proportional to $\exp(-n\ell)$. We allow for infinitely many global minimal points of $\ell$, as long as they form a finite union of compact manifolds. In this scenario, we show estimates for the $p$-Wasserstein convergence of $\left(μ_n\right)_{n \in \mathbb{N}}$ to its limit measure. Imposing regularity conditions we obtain a speed of convergence of $n^{-1/(2p)}$ and adding a further technical assumption, we can improve this to a $p$-independent rate of $1/2$ for all orders $p\in\mathbb{N}$ of the Wasserstein distance.

math.PR↗