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

Pieschner, Susanne; Fuchs, Christiane

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

Pieschner S, Fuchs C (2020)
Royal Society Open Science 7(10): 200270.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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DOI

https://doi.org/10.1098/rsos.200270

Autor*in

Pieschner, Susanne; Fuchs, Christiane^UniBi

Einrichtung

Fakultät für Wirtschaftswissenschaften > Lehrstuhl für Data Science

Projekt

Uncertainty Quantification - From Data to Reliable Knowledge

Abstract / Bemerkung

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.

Erscheinungsjahr

2020

Zeitschriftentitel

Royal Society Open Science

Band

Ausgabe

Art.-Nr.

200270

eISSN

2054-5703

Page URI

https://pub.uni-bielefeld.de/record/2946421

Zitieren

Pieschner S, Fuchs C. Bayesian inference for diffusion processes: using higher-order approximations for transition densities. Royal Society Open Science. 2020;7(10): 200270.

Pieschner, S., & Fuchs, C. (2020). Bayesian inference for diffusion processes: using higher-order approximations for transition densities. Royal Society Open Science, 7(10), 200270. https://doi.org/10.1098/rsos.200270

Pieschner, Susanne, and Fuchs, Christiane. 2020. “Bayesian inference for diffusion processes: using higher-order approximations for transition densities”. Royal Society Open Science 7 (10): 200270.

Pieschner, S., and Fuchs, C. (2020). Bayesian inference for diffusion processes: using higher-order approximations for transition densities. Royal Society Open Science 7:200270.

Pieschner, S., & Fuchs, C., 2020. Bayesian inference for diffusion processes: using higher-order approximations for transition densities. Royal Society Open Science, 7(10): 200270.

S. Pieschner and C. Fuchs, “Bayesian inference for diffusion processes: using higher-order approximations for transition densities”, Royal Society Open Science, vol. 7, 2020, : 200270.

Pieschner, S., Fuchs, C.: Bayesian inference for diffusion processes: using higher-order approximations for transition densities. Royal Society Open Science. 7, : 200270 (2020).

Pieschner, Susanne, and Fuchs, Christiane. “Bayesian inference for diffusion processes: using higher-order approximations for transition densities”. Royal Society Open Science 7.10 (2020): 200270.

Daten bereitgestellt von European Bioinformatics Institute (EBI)