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Componentwise adaptation for high dimensional MCMC

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Summary

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.

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Acknowledgments

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.

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Authors and Affiliations

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

    Heikki Haario

  2. University of Jyväskylä Department of Mathematics and Statistics, University of Jyväskylä, P.O.Box 35 (MaD), FIN-40014, Finland

    Eero Saksman

  3. Finnish Meteorological Institute Geophysical Research Division, 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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Haario, H., Saksman, E. & Tamminen, J. Componentwise adaptation for high dimensional MCMC. Computational Statistics 20, 265–273 (2005). https://doi.org/10.1007/BF02789703

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