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Reversibility of elliptical slice sampling revisited
May 7, 2024, 4:45 a.m. | Mareike Hasenpflug, Viacheslav Telezhnikov, Daniel Rudolf
cs.LG updates on arXiv.org arxiv.org
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.
abstract alternative arxiv cs.lg discuss kernel markov math.st positive property sampling semi show slice spaces stat.co stat.ml stat.th transition type
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