Reversibility of elliptical slice sampling revisited

• URL: http://arxiv.org/abs/2301.02426v2
• Date: Mon, 6 May 2024 11:39:28 GMT
• Title: Reversibility of elliptical slice sampling revisited
• Authors: Mareike Hasenpflug, Viacheslav Telezhnikov, Daniel Rudolf,
• Abstract summary: We extend elliptical slice sampling to infinite-dimensional separable Hilbert spaces and discuss its well-definedness. Crucial within the proof of the formerly mentioned results is the analysis of a shrinkage Markov chain that may be interesting on its own.
• Score: 1.0923877073891446
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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