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
Autor*in
Pieschner, Susanne; Fuchs, ChristianeUniBi
Einrichtung
Fakultät für Wirtschaftswissenschaften > Lehrstuhl für Data Science
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
7
Ausgabe
10
Art.-Nr.
200270
eISSN
2054-5703
Page URI
https://pub.uni-bielefeld.de/record/2946421

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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.
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