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Markov Chain Monte Carlo for Exact Inference for Diffusions

Sermaidis, G; Papaspiliopoulos, O; Roberts, GO; Beskos, A; Fearnhead, P; (2013) Markov Chain Monte Carlo for Exact Inference for Diffusions. Scandinavian Journal of Statistics , 40 (2) pp. 294-321. 10.1111/j.1467-9469.2012.00812.x. Green open access

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Abstract

We develop exact Markov chain Monte Carlo methods for discretely sampled, directly and indirectly observed diffusions. The qualification 'exact' refers to the fact that the invariant and limiting distribution of the Markov chains is the posterior distribution of the parameters free of any discretization error. The class of processes to which our methods directly apply are those which can be simulated using the most general to date exact simulation algorithm. The article introduces various methods to boost the performance of the basic scheme, including reparametrizations and auxiliary Poisson sampling. We contrast both theoretically and empirically how this new approach compares to irreducible high frequency imputation, which is the state-of-the-art alternative for the class of processes we consider, and we uncover intriguing connections. All methods discussed in the article are tested on typical examples. © 2012 Board of the Foundation of the Scandinavian Journal of Statistics.

Type: Article
Title: Markov Chain Monte Carlo for Exact Inference for Diffusions
Open access status: An open access version is available from UCL Discovery
DOI: 10.1111/j.1467-9469.2012.00812.x
Publisher version: http://dx.doi.org/10.1111/j.1467-9469.2012.00812.x
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: Gaussian measure, di�usion process, covariance operator, Hamiltonian dynamics, mixing time, stochastic volatility
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/10045549
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