UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

Advanced MCMC methods for sampling on diffusion pathspace

Beskos, A; Kalogeropoulos, K; Pazos, E; (2013) Advanced MCMC methods for sampling on diffusion pathspace. Stochastic Processes and their Applications , 123 (4) pp. 1415-1453. 10.1016/j.spa.2012.12.001. Green open access

[img]
Preview
Text
Beskos_KalogeropoulosPazos.pdf - Accepted version

Download (297kB) | Preview

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.

Type: Article
Title: Advanced MCMC methods for sampling on diffusion pathspace
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.spa.2012.12.001
Publisher version: http://dx.doi.org/10.1016/j.spa.2012.12.001
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Mathematics, Gaussian measure, Diffusion process, Covariance operator, Hamiltonian dynamics, Mixing time, Stochastic volatility, STOCHASTIC DIFFERENTIAL-EQUATIONS, LIKELIHOOD-BASED INFERENCE, PSEUDO-MARGINAL APPROACH, MONTE-CARLO METHODS, MULTIVARIATE DIFFUSIONS, BAYESIAN-INFERENCE, MODELS, VOLATILITY, ALGORITHM, OPTIONS
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10045547
Downloads since deposit
29Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item