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A multiple-try Metropolis–Hastings algorithm with tailored proposals

Author

Listed:
  • Xin Luo

    (Norwegian University of Science and Technology)

  • Håkon Tjelmeland

    (Norwegian University of Science and Technology)

Abstract

We present a new multiple-try Metropolis–Hastings algorithm designed to be especially beneficial when a tailored proposal distribution is available. The algorithm is based on a given acyclic graph $$\mathcal {G}$$ G , where one of the nodes in $$\mathcal {G}$$ G , k say, contains the current state of the Markov chain and the remaining nodes contain proposed states generated by applying the tailored proposal distribution. The Metropolis–Hastings algorithm alternates between two types of updates. The first type of update is using the tailored proposal distribution to generate new states for all nodes in $$\mathcal {G}$$ G except node k. The second type of update is generating a new value for k, thereby changing the value of the current state. We evaluate the effectiveness of the proposed scheme in two examples with previously defined target and proposal distributions.

Suggested Citation

  • Xin Luo & Håkon Tjelmeland, 2019. "A multiple-try Metropolis–Hastings algorithm with tailored proposals," Computational Statistics, Springer, vol. 34(3), pages 1109-1133, September.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:3:d:10.1007_s00180-019-00878-y
    DOI: 10.1007/s00180-019-00878-y
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    References listed on IDEAS

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    1. Cressie, Noel & Davidson, Jennifer L., 1998. "Image analysis with partially ordered markov models," Computational Statistics & Data Analysis, Elsevier, vol. 29(1), pages 1-26, November.
    2. Hakon Tjelmeland & Bjorn Kare Hegstad, 2001. "Mode Jumping Proposals in MCMC," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 205-223, March.
    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. Chib, Siddhartha & Ramamurthy, Srikanth, 2010. "Tailored randomized block MCMC methods with application to DSGE models," Journal of Econometrics, Elsevier, vol. 155(1), pages 19-38, March.
    5. L. Martino & F. Louzada, 2017. "Issues in the Multiple Try Metropolis mixing," Computational Statistics, Springer, vol. 32(1), pages 239-252, March.
    6. 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.
    7. 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.
    8. 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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    3. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.

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