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Issues in the Multiple Try Metropolis mixing

Author

Listed:
  • L. Martino

    (Universidade de São Paulo)

  • F. Louzada

    (Universidade de São Paulo)

Abstract

The Multiple Try Metropolis (MTM) algorithm is an advanced MCMC technique based on drawing and testing several candidates at each iteration of the algorithm. One of them is selected according to certain weights and then it is tested according to a suitable acceptance probability. Clearly, since the computational cost increases as the employed number of tries grows, one expects that the performance of an MTM scheme improves as the number of tries increases, as well. However, there are scenarios where the increase of number of tries does not produce a corresponding enhancement of the performance. In this work, we describe these scenarios and then we introduce possible solutions for solving these issues.

Suggested Citation

  • L. Martino & F. Louzada, 2017. "Issues in the Multiple Try Metropolis mixing," Computational Statistics, Springer, vol. 32(1), pages 239-252, March.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:1:d:10.1007_s00180-016-0643-9
    DOI: 10.1007/s00180-016-0643-9
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    References listed on IDEAS

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    1. Jean-Marie Cornuet & Jean-Michel Marin & Antonietta Mira & Christian P. Robert, 2012. "Adaptive Multiple Importance Sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 798-812, December.
    2. Bédard, Mylène & Douc, Randal & Moulines, Eric, 2012. "Scaling analysis of multiple-try MCMC methods," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 758-786.
    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. repec:dau:papers:123456789/10690 is not listed on IDEAS
    5. 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.
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    Cited by:

    1. Xin Luo & Håkon Tjelmeland, 2019. "A multiple-try Metropolis–Hastings algorithm with tailored proposals," Computational Statistics, Springer, vol. 34(3), pages 1109-1133, September.
    2. F. Din-Houn Lau & Sebastian Krumscheid, 2022. "Plateau proposal distributions for adaptive component-wise multiple-try metropolis," METRON, Springer;Sapienza Università di Roma, vol. 80(3), pages 343-370, December.

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