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Advanced MCMC methods for sampling on diffusion pathspace

Beskos, Alexandros, Kalogeropoulos, Konstantinos ORCID: 0000-0002-0330-9105 and Pazos, Erik (2013) Advanced MCMC methods for sampling on diffusion pathspace. Stochastic Processes and Their Applications, 123 (4). pp. 1415-1453. ISSN 0304-4149

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Identification Number: 10.1016/j.spa.2012.12.001

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 it’s 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.

Item Type: Article
Official URL: http://www.journals.elsevier.com/stochastic-proces...
Additional Information: © 2012 Elsevier B.V.
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 05 Dec 2012 09:17
Last Modified: 20 Oct 2021 03:16
URI: http://eprints.lse.ac.uk/id/eprint/46433

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