Adaptive proposal distribution for random walk Metropolis algorithm

Computational Statistics volume 14, pages375–395(1999)Cite this article

Summary

The choice of a suitable MCMC method and further the choice of a proposal distribution is known to be crucial for the convergence of the Markov chain. However, in many cases the choice of an effective proposal distribution is difficult. As a remedy we suggest a method called Adaptive Proposal (AP). Although the stationary distribution of the AP algorithm is slightly biased, it appears to provide an efficient tool for, e.g., reasonably low dimensional problems, as typically encountered in non-linear regression problems in natural sciences. As a realistic example we include a successful application of the AP algorithm in parameter estimation for the satellite instrument ‘GOMOS’. In this paper we also present systematic performance criteria for comparing Adaptive Proposal algorithm with more traditional Metropolis algorithms.

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Acknowledgments

The second author (E.S) has been supported by the Academy of Finland, Project 32837. We thank Elja Arjas, Esa Nummelin and Antti Penttinen for useful discussions on the topics of the paper.

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Affiliations

  1. Department of Mathematics, University of Helsinki, P.O.Box 4, Yliopistonkatu 5, FIN-00014, Helsinki, Finland

    Heikki Haario & Eero Saksman

  2. Geophysical Research Division, Finnish Meteorological Insitute, P.O.Box 503, FIN-00101, Helsinki, Finland

    Johanna Tamminen

Authors
  1. Heikki Haario
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  2. Eero Saksman
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  3. Johanna Tamminen
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Correspondence to Heikki Haario.

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Haario, H., Saksman, E. & Tamminen, J. Adaptive proposal distribution for random walk Metropolis algorithm. Computational Statistics 14, 375–395 (1999). https://doi.org/10.1007/s001800050022

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Keywords

  • MCMC
  • Adaptive MCMC
  • Metropolis—Hastings algorithm
  • convergence