The Slice Sampler

  • Christian P. Robert
  • George Casella
Part of the Springer Texts in Statistics book series (STS)


While many of the MCMC algorithms presented in the previous chapter are both generic and universal, there exists a special class of MCMC algorithms that are more model dependent in that they exploit the local conditional features of the distributions to simulate. Before starting the general description of such algorithms, gathered under the (somewhat inappropriate) name of Gibbs sampling, we provide in this chapter a simpler introduction to these special kind of MCMC algorithms. We reconsider the fundamental theorem of simulation (Theorem 2.15) in light of the possibilities opened by MCMC methodology and construct the corresponding slice sampler.


Gibbs Sampler Fundamental Theorem Transition Kernel Slice Sampler Total Variation Distance 
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  1. Neal, R. (1997). Markov chain Monte Carlo methods based on “slicing” the density function. Technical report, Univ. of Toronto.Google Scholar
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  3. Mira, A., Moller, J., and Roberts, G. (2003). Perfect slice samplers. J. Royal Statist. Soc. Series B, 63: 583–606.Google Scholar
  4. Roberts, G. and Rosenthal, J. (2003). The polar slice sampler. Stochastic Models, 18: 257–236.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Christian P. Robert
    • 1
  • George Casella
    • 2
  1. 1.CEREMADEUniversité Paris DauphineParis Cedex 16France
  2. 2.Department of StatisticsUniversity of FloridaGainesvilleUSA

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