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On the flexibility of the design of multiple try Metropolis schemes

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  • Luca Martino
  • Jesse Read

Abstract

The multiple try Metropolis (MTM) method is a generalization of the classical Metropolis–Hastings algorithm in which the next state of the chain is chosen among a set of samples, according to normalized weights. In the literature, several extensions have been proposed. In this work, we show and remark upon the flexibility of the design of MTM-type methods, fulfilling the detailed balance condition. We discuss several possibilities, show different numerical simulations and discuss the implications of the results. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:6:p:2797-2823
    DOI: 10.1007/s00180-013-0429-2
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    References listed on IDEAS

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    1. 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.
    2. Antonietta Mira, 2001. "On Metropolis-Hastings algorithms with delayed rejection," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3-4), pages 231-241.
    3. 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.
    4. 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. 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.
    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. Richard G. Everitt, 2018. "Efficient importance sampling in low dimensions using affine arithmetic," Computational Statistics, Springer, vol. 33(1), pages 1-29, March.

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