Diagnosing Convergence

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


The two previous chapters have presented the theoretical foundations of MCMC algorithms and showed that under fairly general conditions, the chains produced by these algorithms are ergodic, or even geometrically ergodic. While such developments are obviously necessary, they are nonetheless insufficient from the point of view of the implementation of MCMC methods. They do not directly result in methods of controlling the chain produced by an algorithm (in the sense of a stopping rule to guarantee that the number of iterations is sufficient). In other words, general convergence results do not tell us when to stop the MCMC algorithm and produce our estimates.


Markov Chain Stationary Distribution Gibbs Sampling Importance Sampling 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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