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An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift

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  • Yves Atchade

    (Department of Mathematics and Statistics, University of Ottawa and LRSP)

Abstract

This paper proposes an adaptive version for the Metropolis adjusted Langevin algorithm with a truncated drift (T-MALA). The scale parameter and the covariance matrix of the proposal kernel of the algorithm are simultaneously and recursively updated in order to reach the optimal acceptance rate of 0:574 (see Roberts and Rosenthal (2001)) and to estimate and use the correlation structure of the target distribution. We develop some convergence results for the algorithm. A simulation example is presented.

Suggested Citation

  • Yves Atchade, 2005. "An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift," RePAd Working Paper Series LRSP-WP1, Département des sciences administratives, UQO.
    • Handle: RePEc:pqs:wpaper:0272005
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    File URL: http://www.repad.org/ca/on/lrsp/csa2.pdf
    File Function: First version, 2005
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    References listed on IDEAS

    as
    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.
    2. James Davidson & Robert de Jong, 1997. "Strong laws of large numbers for dependent heterogeneous processes: a synthesis of recent and new results," Econometric Reviews, Taylor & Francis Journals, vol. 16(3), pages 251-279.
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    More about this item

    Keywords

    Markov Chain Monte Carlo; Stochastic approximation algorithms; Metropolis Adjusted Langevin algorithm; geometric rate of convergence.;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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