Convergence of slice sampler Markov chains by

@inproceedings{Roberts1999ConvergenceOS,
  title={Convergence of slice sampler Markov chains by},
  author={Gareth O. Roberts and Jeffrey S. Rosenthal},
  year={1999}
}
In this paper, 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 deduce analytic bounds on the total variation distance from stationarity of the method using Foster-Lyapunov drift condition methodology. 

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