I am a third-year PhD student in mathematics, working on slice sampling under joint supervision of Michael Habeck and Daniel Rudolf. My PhD project is associated with both the Interactive Inference project and the Collaborative Research Center 1456 Mathematics of Experiment.

Slice sampling is a class of Markov chain Monte Carlo (MCMC) methods for approximate sampling from (absolutely continuous) probability distributions on (potentially high-dimensional) Euclidean spaces. It can generally be divided into two-subclasses, ideal slice sampling and pragmatic slice sampling. Methods in the former are conceptually simple and correspondingly well-analyzable, but parts of their transition mechanism cannot be efficiently implemented (except in some toy settings), which prevents them from being used in practical applications. Pragmatic slice sampling methods on the other hand are specifically designed to be efficiently implementable, while each mimicking a specific ideal slice sampler in hopes of retaining some of its properties, and have found good use in a variety of practical applications. However, the commitment to computational efficiency has so far only led to methods that are conceptually quite complicated (at least compared to their ideal slice sampling counterparts) and correspondingly hard to formally analyze.

My PhD project concerns itself both with ideal and with pragmatic slice sampling methods. On the one hand, we aim to further improve the theoretical understanding of ideal slice sampling methods, for example by deriving better estimates of their spectral gap, which is known to quantify both the convergence speed and the asymptotic sample quality of an MCMC method for a given target distribution. In our view, results in this regard serve both to underline advantages of slice sampling over other MCMC approaches and to point out performance disparities between different ideal slice samplers.

On the other hand, we are interested in the development of new pragmatic slice sampling methods. By mimicking previously underexplored ideal slice samplers (such as polar slice sampling), we hope to devise new MCMC methods that, at least in certain types of settings, outperform all existing ones. This in turn necessitates some theoretical work, because for pragmatic slice samplers merely proving their asymptotic convergence already poses a significant challenge. However, most of the work in this area consists of numerical experiments, because (in light of their being so difficult to formally analyze) pragmatic slice samplers are mostly evaluated based on their empirical performance, both in synthetic settings and in real world applications.

My Pages

arXiv Publications
Google Scholar
Research Gate
Semantic Scholar
LinkedIn

Publications

• A dimension-independent bound on the Wasserstein contraction rate of a geodesic random walk on the sphere
  Philip Schär, Thilo Stier
  Electronic Communications in Probability 29, article 62, 2024
  Link to Paper

• Parallel affine transformation tuning of Markov chain Monte Carlo
  Philip Schär, Michael Habeck, Daniel Rudolf
  Proceedings of the 41st International Conference on Machine Learning (ICML).
  PMLR 235, pp. 43571-43607, 2024
  Link to Paper
  Link to Source Code

• Wasserstein contraction and spectral gap of slice sampling revisited
  Philip Schär
  Electronic Journal of Probability 28, article 136, 2023
  Link to Paper

• Dimension-independent spectral gap of polar slice sampling
  Daniel Rudolf, Philip Schär
  Statistics and Computing 34(1), article 20, 2024
  Link to Paper

• Gibbsian polar slice sampling
  Philip Schär, Michael Habeck, Daniel Rudolf
  Proceedings of the 40th International Conference on Machine Learning (ICML),
  PMLR 202, pp. 30204-30223, 2023
  Link to Paper
  Link to Source Code