Convergence of slice sampler Markov chains.

Roberts, G. O. and Rosenthal, J. S. (1999) Convergence of slice sampler Markov chains. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 61 (3). pp. 643-660. ISSN 1467-9868

Abstract

We analyse theoretical properties of the slice sampler. We find that the algorithm has extremely robust geometric ergodicity properties. For the case of just one auxiliary variable, we demonstrate that the algorithm is stochastically monotone, and we deduce analytic bounds on the total variation distance from stationarity of the method by using Foster–Lyapunov drift condition methodology.