Bayesian inference for diffusion processes: using higher-order approximations for transition densities
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 appr...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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The Royal Society
2020-10-01
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| Series: | Royal Society Open Science |
| Subjects: | |
| Online Access: | https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.200270 |
| _version_ | 1818348068762812416 |
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| author | Susanne Pieschner Christiane Fuchs |
| author_facet | Susanne Pieschner Christiane Fuchs |
| author_sort | Susanne Pieschner |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-13T17:44:11Z |
| format | Article |
| id | doaj.art-9350c25d231e4584afc546a4b4bcc498 |
| institution | Directory Open Access Journal |
| issn | 2054-5703 |
| language | English |
| last_indexed | 2024-12-13T17:44:11Z |
| publishDate | 2020-10-01 |
| publisher | The Royal Society |
| record_format | Article |
| series | Royal Society Open Science |
| spelling | doaj.art-9350c25d231e4584afc546a4b4bcc4982022-12-21T23:36:39ZengThe Royal SocietyRoyal Society Open Science2054-57032020-10-0171010.1098/rsos.200270200270Bayesian inference for diffusion processes: using higher-order approximations for transition densitiesSusanne PieschnerChristiane FuchsModelling 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.https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.200270stochastic differential equationsmarkov chain monte carlomilstein schemeparameter estimationbayesian data imputation |
| spellingShingle | Susanne Pieschner Christiane Fuchs Bayesian inference for diffusion processes: using higher-order approximations for transition densities Royal Society Open Science stochastic differential equations markov chain monte carlo milstein scheme parameter estimation bayesian data imputation |
| title | Bayesian inference for diffusion processes: using higher-order approximations for transition densities |
| title_full | Bayesian inference for diffusion processes: using higher-order approximations for transition densities |
| title_fullStr | Bayesian inference for diffusion processes: using higher-order approximations for transition densities |
| title_full_unstemmed | Bayesian inference for diffusion processes: using higher-order approximations for transition densities |
| title_short | Bayesian inference for diffusion processes: using higher-order approximations for transition densities |
| title_sort | bayesian inference for diffusion processes using higher order approximations for transition densities |
| topic | stochastic differential equations markov chain monte carlo milstein scheme parameter estimation bayesian data imputation |
| url | https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.200270 |
| work_keys_str_mv | AT susannepieschner bayesianinferencefordiffusionprocessesusinghigherorderapproximationsfortransitiondensities AT christianefuchs bayesianinferencefordiffusionprocessesusinghigherorderapproximationsfortransitiondensities |