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Plateau proposal distributions for adaptive component-wise multiple-try metropolis

Author

Listed:
  • F. Din-Houn Lau
  • Sebastian Krumscheid

    (RWTH Aachen University)

Abstract

Markov chain Monte Carlo (MCMC) methods are sampling methods that have become a commonly used tool in statistics, for example to perform Monte Carlo integration. As a consequence of the increase in computational power, many variations of MCMC methods exist for generating samples from arbitrary, possibly complex, target distributions. The performance of an MCMC method, in particular that of a Metropolis–Hastings MCMC method, is predominately governed by the choice of the so-called proposal distribution used. In this paper, we introduce a new type of proposal distribution for the use in Metropolis–Hastings MCMC methods that operates component-wise and with multiple trials per iteration. Specifically, the novel class of proposal distributions, called Plateau distributions, does not overlap, thus ensuring that the multiple trials are drawn from different regions of the state space. Furthermore, the Plateau proposal distributions allow for a bespoke adaptation procedure that lends itself to a Markov chain with efficient problem dependent state space exploration and favourable burn-in properties. Simulation studies show that our novel MCMC algorithm outperforms competitors when sampling from distributions with a complex shape, highly correlated components or multiple modes.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metron:v:80:y:2022:i:3:d:10.1007_s40300-022-00235-y
    DOI: 10.1007/s40300-022-00235-y
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    References listed on IDEAS

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    1. 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.
    2. L. Martino & F. Louzada, 2017. "Issues in the Multiple Try Metropolis mixing," Computational Statistics, Springer, vol. 32(1), pages 239-252, March.
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