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A multi-point Metropolis scheme with generic weight functions

Author

Listed:
  • Martino, Luca
  • Del Olmo, Victor Pascual
  • Read, Jesse

Abstract

The multi-point Metropolis algorithm is an advanced MCMC technique based on drawing several correlated samples at each step and choosing one of them according to some normalized weights. We propose a variation of this technique where the weight functions are not specified, i.e., the analytic form can be chosen arbitrarily. This has the advantage of greater flexibility in the design of high-performance MCMC samplers. We prove that our method fulfills the balance condition, and provide a numerical simulation. We also give new insight into the functionality of different MCMC algorithms, and the connections between them.

Suggested Citation

  • Martino, Luca & Del Olmo, Victor Pascual & Read, Jesse, 2012. "A multi-point Metropolis scheme with generic weight functions," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1445-1453.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:7:p:1445-1453
    DOI: 10.1016/j.spl.2012.04.008
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    References listed on IDEAS

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    1. Geir Storvik, 2011. "On the Flexibility of Metropolis–Hastings Acceptance Probabilities in Auxiliary Variable Proposal Generation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(2), pages 342-358, June.
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    Cited by:

    1. L. Martino & F. Louzada, 2017. "Issues in the Multiple Try Metropolis mixing," Computational Statistics, Springer, vol. 32(1), pages 239-252, March.
    2. Xin Luo & Håkon Tjelmeland, 2019. "A multiple-try Metropolis–Hastings algorithm with tailored proposals," Computational Statistics, Springer, vol. 34(3), pages 1109-1133, September.
    3. Luca Martino & Jesse Read, 2013. "On the flexibility of the design of multiple try Metropolis schemes," Computational Statistics, Springer, vol. 28(6), pages 2797-2823, December.
    4. 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".
    5. Pandolfi, Silvia & Bartolucci, Francesco & Friel, Nial, 2014. "A generalized multiple-try version of the Reversible Jump algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 298-314.
    6. Wei Shao & Yijun Zuo, 2020. "Computing the halfspace depth with multiple try algorithm and simulated annealing algorithm," Computational Statistics, Springer, vol. 35(1), pages 203-226, March.

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