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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. 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.
    2. 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.
    3. 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.
    4. 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. 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".
    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. L. Martino & F. Louzada, 2017. "Issues in the Multiple Try Metropolis mixing," Computational Statistics, Springer, vol. 32(1), pages 239-252, March.
    4. Richard G. Everitt, 2018. "Efficient importance sampling in low dimensions using affine arithmetic," Computational Statistics, Springer, vol. 33(1), pages 1-29, March.
    5. 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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