Robust adaptive Metropolis algorithm with coerced acceptance rate

Statistics and Computing volume 22, pages997–1008(2012)Cite this article

Abstract

The adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen (Bernoulli 7(2):223–242, 2001) uses the estimated covariance of the target distribution in the proposal distribution. This paper introduces a new robust adaptive Metropolis algorithm estimating the shape of the target distribution and simultaneously coercing the acceptance rate. The adaptation rule is computationally simple adding no extra cost compared with the AM algorithm. The adaptation strategy can be seen as a multidimensional extension of the previously proposed method adapting the scale of the proposal distribution in order to attain a given acceptance rate. The empirical results show promising behaviour of the new algorithm in an example with Student target distribution having no finite second moment, where the AM covariance estimate is unstable. In the examples with finite second moments, the performance of the new approach seems to be competitive with the AM algorithm combined with scale adaptation.

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  1. Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, 40014, University of Jyväskylä, Finland

    Matti Vihola

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  1. Matti Vihola
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Correspondence to Matti Vihola.

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Vihola, M. Robust adaptive Metropolis algorithm with coerced acceptance rate. Stat Comput 22, 997–1008 (2012). https://doi.org/10.1007/s11222-011-9269-5

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Keywords

  • Acceptance rate
  • Adaptive Markov chain Monte Carlo
  • Ergodicity
  • Metropolis algorithm
  • Robustness