Gibbsian polar slice sampling

Michael Habeck, Philip Schär, Daniel Rudolf

Publication date: 8 February 2023

Abstract: Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension. By updating the directional and radial components of chain iterates separately, we obtain a family of samplers that mimic polar slice sampling, and yet can be implemented efficiently. Numerical experiments in a variety of settings indicate that our proposed algorithm outperforms the two most closely related approaches, elliptical slice sampling (Murray et al., 2010) and hit-and-run uniform slice sampling (MacKay, 2003). We prove the well-definedness and convergence of our methods under suitable assumptions on the target distribution.

Has companion code repository: https://github.com/microscopic-image-analysis/gibbsian_polar_slice_sampling

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Monte Carlo methods (65C05) Discrete-time Markov processes on general state spaces (60J05)

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