Reversibility of elliptical slice sampling revisited
This work addresses theoretical foundations for sampling methods in high-dimensional spaces, but it is incremental as it revisits and extends an existing technique.
The paper extends elliptical slice sampling to infinite-dimensional Hilbert spaces, ensuring its well-definedness and proving reversibility, which induces a positive semi-definite Markov operator.
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.