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Scaling Analysis of Delayed Rejection MCMC Methods

Author

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  • Mylène Bédard

    (Université de Montréal)

  • Randal Douc

    (SAMOVAR, CNRS UMR 5157 - Institut Télécom/Télécom SudParis)

  • Eric Moulines

    (LTCI, CNRS UMR 8151 - Institut Télécom /Télécom ParisTech)

Abstract

In this paper, we study the asymptotic efficiency of the delayed rejection strategy. In particular, the efficiency of the delayed rejection Metropolis–Hastings algorithm is compared to that of the regular Metropolis algorithm. To allow for a fair comparison, the study is carried under optimal mixing conditions for each of these algorithms. After introducing optimal scaling results for the delayed rejection (DR) algorithm, we outline the fact that the second proposal after the first rejection is discarded, with a probability tending to 1 as the dimension of the target density increases. To overcome this drawback, a modification of the delayed rejection algorithm is proposed, in which the direction of the different proposals is fixed once for all, and the Metropolis–Hastings accept-reject mechanism is used to select a proper scaling along the search direction. It is shown that this strategy significantly outperforms the original DR and Metropolis algorithms, especially when the dimension becomes large. We include numerical studies to validate these conclusions.

Suggested Citation

  • Mylène Bédard & Randal Douc & Eric Moulines, 2014. "Scaling Analysis of Delayed Rejection MCMC Methods," Methodology and Computing in Applied Probability, Springer, vol. 16(4), pages 811-838, December.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:4:d:10.1007_s11009-013-9326-y
    DOI: 10.1007/s11009-013-9326-y
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    References listed on IDEAS

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    1. Davide Raggi, 2005. "Adaptive MCMC methods for inference on affine stochastic volatility models with jumps," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 235-250, July.
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    Cited by:

    1. Marcel F. Jonker & Arthur E. Attema & Bas Donkers & Elly A. Stolk & Matthijs M. Versteegh, 2017. "Are Health State Valuations from the General Public Biased? A Test of Health State Reference Dependency Using Self‐assessed Health and an Efficient Discrete Choice Experiment," Health Economics, John Wiley & Sons, Ltd., vol. 26(12), pages 1534-1547, December.
    2. Bédard, Mylène, 2017. "Hierarchical models: Local proposal variances for RWM-within-Gibbs and MALA-within-Gibbs," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 231-246.

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