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Adaptive Sticky Generalized Metropolis

Author

Listed:
  • Fabrizio Leisen

    (University of Kent)

  • Roberto Casarin

    (University of Venice C� Foscari)

  • David Luengo

    (Universidad Politecnica de Madrid)

  • Luca Martino

    (Universidad Carlos III de Madrid)

Abstract

We introduce a new class of adaptive Metropolis algorithms called adaptive sticky algorithms for efficient general-purpose simulation from a target probability distribution. The transition of the Metropolis chain is based on a multiple-try scheme and the different proposals are generated by adaptive nonparametric distributions. Our adaptation strategy uses the interpolation of support points from the past history of the chain as in the adaptive rejection Metropolis. The algorithm efficiency is strengthened by a step that controls the evolution of the set of support points. This extra stage improves the computational cost and accelerates the convergence of the proposal distribution to the target. Despite the algorithms are presented for univariate target distributions, we show that they can be easily extended to the multivariate context by a Gibbs sampling strategy. We show the ergodicity of the proposed algorithms and illustrate their efficiency and effectiveness through some simulated examples involving target distributions with complex structures.

Suggested Citation

  • Fabrizio Leisen & Roberto Casarin & David Luengo & Luca Martino, 2013. "Adaptive Sticky Generalized Metropolis," Working Papers 2013:19, Department of Economics, University of Venice "Ca' Foscari".
    • Handle: RePEc:ven:wpaper:2013:19
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    References listed on IDEAS

    as
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    2. Shao, Wei & Guo, Guangbao & Meng, Fanyu & Jia, Shuqin, 2013. "An efficient proposal distribution for Metropolis–Hastings using a B-splines technique," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 465-478.
    3. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    4. Casarin, Roberto & Craiu, Radu & Leisen, Fabrizio, 2011. "Interacting multiple -- Try algorithms with different proposal distributions," DES - Working Papers. Statistics and Econometrics. WS ws110402, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. repec:dau:papers:123456789/6072 is not listed on IDEAS
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    Full references (including those not matched with items on IDEAS)

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    Keywords

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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