Reversibility of elliptical slice sampling revisited

arXiv:2301.02426v2 Announce Type: replace-cross
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