Variable Dimension Models and Reversible Jump Algorithms

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


While the previous chapters have presented a general class of MCMC algorithms, there exist settings where they are not general enough. A particular case of such settings is that of variable dimension models. There, the parameter (and simulation) space is not well defined, being a finite or denumerable collection of unrelated subspaces. To have an MCMC algorithm moving within this collection of spaces requires more advanced tools, if only because of the associated measure theoretic subtleties. Section 11.1 motivates the use of variable dimension models in the setup of Bayesian model choice and model comparison, while Section 11.2 presents the general theory of reversible jump algorithms, which were tailored for these models. Section 11.3 examines further algorithms and methods related to this issue.


Posterior Distribution Prior Distribution Acceptance Probability Markov Jump Process MCMC Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adams, M. (1987). William Ockham. University of Notre Dame Press, Notre Dame, Indiana.Google Scholar
  2. Wolpert, D. (1992). A rigorous investigation of evidence and Occam factors in Bayesian reasoning. Technical report, Santa Fe Institute.Google 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

Personalised recommendations