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Pieschner, S. ; Fuchs, C.

Bayesian inference for diffusion processes: Using higher-order approximations for transition densities.

R. Soc. Open Sci. 7:200270 (2020)
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Open Access Gold
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Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods that introduce auxiliary data. These methods typically approximate the transition densities of the process numerically, both for calculating the posterior densities and proposing auxiliary data. Here, the Euler-Maruyama scheme is the standard approximation technique. However, the MCMC method is computationally expensive. Using higher-order approximations may accelerate it, but the specific implementation and benefit remain unclear. Hence, we investigate the utilization and usefulness of higher-order approximations in the example of the Milstein scheme. Our study demonstrates that the MCMC methods based on the Milstein approximation yield good estimation results. However, they are computationally more expensive and can be applied to multidimensional processes only with impractical restrictions. Moreover, the combination of the Milstein approximation and the well-known modified bridge proposal introduces additional numerical challenges.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Bayesian Data Imputation ; Markov Chain Monte Carlo ; Milstein Scheme ; Parameter Estimation ; Stochastic Differential Equations
Sprache englisch
Veröffentlichungsjahr 2020
HGF-Berichtsjahr 2020
ISSN (print) / ISBN 2054-5703
e-ISSN 2054-5703
Zeitschrift Royal Society Open Science
Quellenangaben Band: 7, Heft: 10, Seiten: , Artikelnummer: 200270 Supplement: ,
Verlag Royal Society of London
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Computational Biology (ICB)
POF Topic(s) 30205 - Bioengineering and Digital Health
Forschungsfeld(er) Enabling and Novel Technologies
PSP-Element(e) G-503800-001
Förderungen Bundesministerium für Bildung und Forschung
Deutsche Forschungsgemeinschaft
DOI 10.1098/rsos.200270rsos200270
Scopus ID 85096289842
WOS ID WOS:000582229900001
Erfassungsdatum 2020-11-27
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