Computational Statistics

, Volume 20, Issue 2, pp 265–273 | Cite as

Componentwise adaptation for high dimensional MCMC

  • Heikki Haario
  • Eero Saksman
  • Johanna Tamminen


We introduce a new adaptive MCMC algorithm, based on the traditional single component Metropolis-Hastings algorithm and on our earlier adaptive Metropolis algorithm (AM). In the new algorithm the adaption is performed component by component. The chain is no more Markovian, but it remains ergodic. The algorithm is demonstrated to work well in varying test cases up to 1000 dimensions.


MCMC adaptive MCMC Metropolis-Hastings algorithm 



This work has been supported by the Academy of Finland, MaDaMe project. We would also like to thank Prof. P.J. Green for the code for computing the integrated autocorrelation values.


  1. Andrieu, C. & Robert, C. P. (2001), Controlled MCMC for optimal sampling. Preprint. *http://www. statslab. cam. Scholar
  2. Atchade, Y. F. & Rosenthal, J. S. (2003), On Adaptive Markov Chain Monte Carlo Algorithms. Preprint. *http://www. statslab. cam. ac. uk/mcmc/Google Scholar
  3. Gelman, A. G., Roberts, G. O. & Gilks, W. R. (1996), Efficient Metropolis jumping rules,in J. M. Bernardo, J. O. Berger, A. F. David & A. F. M. Smith, eds, ‘Bayesian Statistics V’, Oxford Univ. Press, New York, pp. 599–608.Google Scholar
  4. Gilks, W. & Roberts, G. (1995), Stategies for improving MCMC,in W. R. Gilks, S. Richardson & D. J. Spiegelhalter, eds, ‘Markov Chain Monte Carlo in Practice’, Chapman & Hall, pp. 75–88.Google Scholar
  5. Gilks, W., Roberts, G. & Sahu, S. (1998), ‘Adaptive Markov chain Monte Carlo through regeneration’,J. Am. Stat. Ass. 93, 1045–1054.MathSciNetCrossRefGoogle Scholar
  6. Haario, H., Saksman, E. & Tamminen, J. (1999), ‘Adaptive proposal distribution for random walk Metropolis algorithm’,Comput. Stat. 14, 375–395.CrossRefGoogle Scholar
  7. Haario, H., Saksman, E. & Tamminen, J. (2001), ‘An adaptive Metropolis algorithm’,Bernoulli 7(2), 223–242.MathSciNetCrossRefGoogle Scholar
  8. Haario, H., Saksman, E. & Tamminen, J. (2003), Componentwise adaptation for MCMC. Reports of the Department of Mathematics, University of Helsinki, Preprint 342.Google Scholar
  9. Hastings, W. (1970), ‘Monte Carlo sampling methods using Markov chains and their applications’,Biometrika 57, 97–109.MathSciNetCrossRefGoogle Scholar
  10. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. & Teller, E. (1953), ‘Equations of state calculations by fast computing machine’,J. Chem. Phys. 21, 1087–1091.CrossRefGoogle Scholar
  11. Sahu, S. K. & Zhigljavsky, A. A. (2003), ‘Self regenerative Markov chain Monte Carlo with adaptation’,Bernoulli pp. 395–422.Google Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Heikki Haario
    • 1
  • Eero Saksman
    • 2
  • Johanna Tamminen
    • 3
  1. 1.University of Helsinki Department of Mathematics and StatisticsUniversity of HelsinkiFinland
  2. 2.University of Jyväskylä Department of Mathematics and StatisticsUniversity of JyväskyläFinland
  3. 3.Finnish Meteorological Institute Geophysical Research DivisionHelsinkiFinland

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