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Advanced MCMC methods for sampling on diffusion pathspace

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  • Beskos, Alexandros
  • Kalogeropoulos, Konstantinos
  • Pazos, Erik

Abstract

The need to calibrate increasingly complex statistical models requires a persistent effort for further advances on available, computationally intensive Monte-Carlo methods. We study here an advanced version of familiar Markov-chain Monte-Carlo (MCMC) algorithms that sample from target distributions defined as change of measures from Gaussian laws on general Hilbert spaces. Such a model structure arises in several contexts: we focus here at the important class of statistical models driven by diffusion paths whence the Wiener process constitutes the reference Gaussian law. Particular emphasis is given on advanced Hybrid Monte-Carlo (HMC) which makes large, derivative-driven steps in the state space (in contrast with local-move Random-walk-type algorithms) with analytical and experimental results. We illustrate its computational advantages in various diffusion processes and observation regimes; examples include stochastic volatility and latent survival models. In contrast with their standard MCMC counterparts, the advanced versions have mesh-free mixing times, as these will not deteriorate upon refinement of the approximation of the inherently infinite-dimensional diffusion paths by finite-dimensional ones used in practice when applying the algorithms on a computer.

Suggested Citation

  • Beskos, Alexandros & Kalogeropoulos, Konstantinos & Pazos, Erik, 2013. "Advanced MCMC methods for sampling on diffusion pathspace," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1415-1453.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:4:p:1415-1453
    DOI: 10.1016/j.spa.2012.12.001
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    Cited by:

    1. Beskos, Alexandros, 2014. "A stable manifold MCMC method for high dimensions," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 46-52.

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    More about this item

    Keywords

    Gaussian measure; Diffusion process; Covariance operator; Hamiltonian dynamics; Mixing time; Stochastic volatility;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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