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On the stability and ergodicity of adaptive scaling Metropolis algorithms


  • Vihola, Matti


The stability and ergodicity properties of two adaptive random walk Metropolis algorithms are considered. Both algorithms adjust the scaling of the proposal distribution continuously based on the observed acceptance probability. Unlike the previously proposed forms of the algorithms, the adapted scaling parameter is not constrained within a predefined compact interval. The first algorithm is based on scale adaptation only, while the second one also incorporates covariance adaptation. A strong law of large numbers is shown to hold assuming that the target density is smooth enough and has either compact support or super-exponentially decaying tails.

Suggested Citation

  • Vihola, Matti, 2011. "On the stability and ergodicity of adaptive scaling Metropolis algorithms," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2839-2860.
  • Handle: RePEc:eee:spapps:v:121:y:2011:i:12:p:2839-2860
    DOI: 10.1016/

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    References listed on IDEAS

    1. Jarner, Søren Fiig & Hansen, Ernst, 2000. "Geometric ergodicity of Metropolis algorithms," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 341-361, February.
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    Cited by:

    1. Mbalawata, Isambi S. & Särkkä, Simo & Vihola, Matti & Haario, Heikki, 2015. "Adaptive Metropolis algorithm using variational Bayesian adaptive Kalman filter," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 101-115.


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