Markov chain Monte Carlo for exact inference for diffusions

Sermaidis, Giorgos and Papaspiliopoulos, Omiros and Roberts, Gareth and Beskos, Alexandros and Fearnhead, Paul (2013) Markov chain Monte Carlo for exact inference for diffusions. Scandinavian Journal of Statistics, 40 (2). pp. 294-321. ISSN 0303-6898

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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.

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Journal Article
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Scandinavian Journal of Statistics
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04 Sep 2014 10:57
Last Modified:
22 Nov 2022 01:05