Componentwise adaptation for high dimensional MCMC
- 1.4k Downloads
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.
KeywordsMCMC 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.
- Andrieu, C. & Robert, C. P. (2001), Controlled MCMC for optimal sampling. Preprint. *http://www. statslab. cam. ac.uk/mcmc/Google Scholar
- Atchade, Y. F. & Rosenthal, J. S. (2003), On Adaptive Markov Chain Monte Carlo Algorithms. Preprint. *http://www. statslab. cam. ac. uk/mcmc/Google Scholar
- 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
- 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
- Haario, H., Saksman, E. & Tamminen, J. (2003), Componentwise adaptation for MCMC. Reports of the Department of Mathematics, University of Helsinki, Preprint 342.Google Scholar
- Sahu, S. K. & Zhigljavsky, A. A. (2003), ‘Self regenerative Markov chain Monte Carlo with adaptation’,Bernoulli pp. 395–422.Google Scholar