Bayesian estimation of ordinary differential equation models when the likelihood has multiple local modes
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Baisen Liu
Abstract
Ordinary differential equations (ODEs) are popularly used to model complex dynamic systems by scientists; however, the parameters in ODE models are often unknown and have to be inferred from noisy measurements of the dynamic system. One conventional method is to maximize the likelihood function, but the likelihood function often has many local modes due to the complexity of ODEs, which makes the optimizing algorithm be vulnerable to trap in local modes. In this paper, we solve the global optimization issue of ODE parameters with the help of the Stochastic Approximation Monte Carlo (SAMC) algorithm which is shown to be self-adjusted and escape efficiently from the “local-trapping” problem. Our simulation studies indicate that the SAMC method is a powerful tool to estimate ODE parameters globally. The efficiency of SAMC method is demonstrated by estimating a predator-prey ODEs model from real experimental data.
Funding source: Natural Sciences and Engineering Research Council of Canada
Award Identifier / Grant number: RGPIN 356044-2013
Award Identifier / Grant number: 435713-2013
Funding statement: The research was supported by the Liaoning Provincial Education Department (No. LN2017ZD001) to Baisen Liu and the discovery grants (RGPIN 356044-2013, 435713-2013) from the Natural Science and Engineering Research Council of Canada to Jiguo Cao and Liangliang Wang.
Acknowledgements
We thank Professor Gregor F. Fussmann for providing us the predator-prey data set. The authors are also very grateful for the suggestions of Professor Faming Liang.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Probability distribution of the life time of a drift-diffusion-reaction process inside a sphere with applications to transient cathodoluminescence imaging
- A quasi-Monte Carlo implementation of the ziggurat method
- On the efficient simulation of the left-tail of the sum of correlated log-normal variates
- Bayesian estimation of ordinary differential equation models when the likelihood has multiple local modes
- On the modeling of linear system input stochastic processes with given accuracy and reliability
- Remarks on randomization of quasi-random numbers
- On average dimensions of particle transport estimators
Artikel in diesem Heft
- Frontmatter
- Probability distribution of the life time of a drift-diffusion-reaction process inside a sphere with applications to transient cathodoluminescence imaging
- A quasi-Monte Carlo implementation of the ziggurat method
- On the efficient simulation of the left-tail of the sum of correlated log-normal variates
- Bayesian estimation of ordinary differential equation models when the likelihood has multiple local modes
- On the modeling of linear system input stochastic processes with given accuracy and reliability
- Remarks on randomization of quasi-random numbers
- On average dimensions of particle transport estimators
