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Langevin type limiting processes for adaptive MCMC

Author

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  • G. K. Basak

    (Indian Statistical Institute)

  • Arunangshu Biswas

    (Presidency University)

Abstract

Adaptive Markov Chain Monte Carlo (AMCMC) is a class of MCMC algorithms where the proposal distribution changes at every iteration of the chain. In this case it is important to verify that such a Markov Chain indeed has a stationary distribution. In this paper we discuss a diffusion approximation to a discrete time AMCMC. This diffusion approximation is different when compared to the diffusion approximation as in Gelman et al. [5] where the state space increases in dimension to ∞. In our approach the time parameter is sped up in such a way that the limiting process (as the mesh size goes to 0) approaches to a non-trivial diffusion process.

Suggested Citation

  • G. K. Basak & Arunangshu Biswas, 2016. "Langevin type limiting processes for adaptive MCMC," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(2), pages 301-328, June.
    • Handle: RePEc:spr:indpam:v:47:y:2016:i:2:d:10.1007_s13226-016-0189-0
    DOI: 10.1007/s13226-016-0189-0
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    References listed on IDEAS

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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. O. Stramer & R. L. Tweedie, 1999. "Langevin-Type Models II: Self-Targeting Candidates for MCMC Algorithms," Methodology and Computing in Applied Probability, Springer, vol. 1(3), pages 307-328, October.
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