Home | Contents | Submissions, editors, etc. | Login | Search | EJP
 Electronic Communications in Probability > Vol. 12 (2007) > Paper 33 open journal systems 


On the efficiency of adaptive MCMC algorithms

Christophe Andrieu, University of Bristol
Yves Atchade, University of Michigan


Abstract
We study a class of adaptive Markov Chain Monte Carlo (MCMC) processes which aim at behaving as an ``optimal'' target process via a learning procedure. We show, under appropriate conditions, that the adaptive MCMC chain and the ``optimal'' (nonadaptive) MCMC process share many asymptotic properties. The special case of adaptive MCMC algorithms governed by stochastic approximation is considered in details and we apply our results to the adaptive Metropolis algorithm of [Haario, Saksman, Tamminen].


Full text: PDF

Pages: 336-349

Published on: October 12, 2007
Bibliography
  1. C. Andrieu. Discussion, ordinary meeting on inverse problems, wednesday 10th december, 2003, london. Journal of the Royal Statistical Society B 66 (2004), 627-652.
  2. Andrieu, Christophe; Moulines, Éric. On the ergodicity properties of some adaptive MCMC algorithms. Ann. Appl. Probab. 16 (2006), no. 3, 1462--1505. MR2260070
  3. Andrieu, Christophe; Moulines, Éric; Priouret, Pierre. Stability of stochastic approximation under verifiable conditions. SIAM J. Control Optim. 44 (2005), no. 1, 283--312 (electronic). MR2177157 (2006f:62074)
  4. C. Andrieu and C. P. Robert. Controlled mcmc for optimal sampling. Technical Report Universit'e Paris Dauphine, Ceremade 0125. (2001).
  5. Atchadé, Yves F.; Rosenthal, Jeffrey S. On adaptive Markov chain Monte Carlo algorithms. Bernoulli 11 (2005), no. 5, 815--828. MR2172842 (2006h:62077)
  6. Baxendale, Peter H. Renewal theory and computable convergence rates for geometrically ergodic Markov chains. Ann. Appl. Probab. 15 (2005), no. 1B, 700--738. MR2114987 (2005m:60164)
  7. Benveniste, Albert; Métivier, Michel; Priouret, Pierre. Adaptive algorithms and stochastic approximations.Translated from the French by Stephen S. Wilson.Applications of Mathematics (New York), 22. Springer-Verlag, Berlin, 1990. xii+365 pp. ISBN: 3-540-52894-6 MR1082341 (92h:62137)
  8. Markov chain Monte Carlo in practice.Edited by W. R. Gilks, S. Richardson and D. J. Spiegelhalter.Interdisciplinary Statistics. Chapman & Hall, London, 1996. xviii+486 pp. ISBN: 0-412-05551-1 MR1397966 (97d:62006)
  9. Gilks, Walter R.; Roberts, Gareth O.; Sahu, Sujit K. Adaptive Markov chain Monte Carlo through regeneration. J. Amer. Statist. Assoc. 93 (1998), no. 443, 1045--1054. MR1649199 (2000f:62063)
  10. Goldstein, Sheldon. Maximal coupling. Z. Wahrsch. Verw. Gebiete 46 (1978/79), no. 2, 193--204. MR0516740 (80k:60041)
  11. Haario, Heikki; Saksman, Eero; Tamminen, Johanna. An adaptive metropolis algorithm. Bernoulli 7 (2001), no. 2, 223--242. MR1828504 (2002c:65008)
  12. H. Kushner and G. Yin. Stochastic approximation and recursive algorithms and Applications. Springer, Springer-Verlag, New-York (2003).
  13. J.S. Rosenthal and G.O. Roberts. Coupling and ergodicity of adaptive mcmc.
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | EJP

Electronic Communications in Probability. ISSN: 1083-589X