The Gibbs Sampler

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


The previous chapter developed simulation techniques that could be called “generic,” since they require only a limited amount of information about the distribution to be simulated. For example, the generic algorithm ARMS (§6.3.3) aims at reproducing the density f of this distribution in an automatic manner. However, Metropolis-Hastings algorithms can achieve higher levels of efficiency when they take into account the specifics of the target distribution f, in particular through the calibration of the acceptance rate (see §6.4.1). Moving even further in this direction, the properties and performance of the Gibbs sampling method presented in this chapter are very closely tied to the distribution f. This is because the choice of instrumental distribution is essentially reduced to a choice between a finite number of possibilities.


Markov Chain Posterior Distribution Conditional Distribution Gibbs Sampler Transition Kernel 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Christian P. Robert
    • 1
    • 2
  • George Casella
    • 3
  1. 1.Laboratoire de StatistiqueCREST-INSEEParis Cedex 14France
  2. 2.Dept. de Mathematique UFR des SciencesUniversite de RouenMont Saint Aignan cedexFrance
  3. 3.Biometrics UnitCornell UniversityIthacaUSA

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