Reversibility of elliptical slice sampling revisited

Mareike Hasenpflug; Viacheslav Telezhnikov; Daniel Rudolf

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arXiv · 2301.02426

Reversibility of elliptical slice sampling revisited

Mareike Hasenpflug·Viacheslav Telezhnikov·Daniel Rudolf

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Abstract

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.

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Mareike Hasenpflug, Viacheslav Telezhnikov, Daniel Rudolf. 2023-01-06. Reversibility of elliptical slice sampling revisited. https://arxiv.org/abs/2301.02426

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