Convergence of Slice Sampler Markov Chains
Gareth O. Roberts, Jeffrey S. Rosenthal
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1999 · Volume 61 · Issue 3
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.
Keywords
Auxiliary variables, Foster–Lyapunov drift condition, Markov chain Monte Carlo methods, Slice sampler
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