Adaptive Semiparametric Bayesian Differential Equations Via Sequential Monte Carlo
| Autor: | Shijia Wang, Shufei Ge, Renny Doig, Liangliang Wang |
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| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Differential equation Computer science B-spline Bayesian probability 010103 numerical & computational mathematics Delay differential equation Statistics - Computation 01 natural sciences 010104 statistics & probability Range (mathematics) Complex dynamic systems Ordinary differential equation Discrete Mathematics and Combinatorics Applied mathematics 0101 mathematics Statistics Probability and Uncertainty Particle filter Computation (stat.CO) |
| Zdroj: | Journal of Computational and Graphical Statistics. 31:600-613 |
| ISSN: | 1537-2715 1061-8600 |
| DOI: | 10.1080/10618600.2021.1987252 |
| Popis: | Nonlinear differential equations (DEs) are used in a wide range of scientific problems to model complex dynamic systems. The differential equations often contain unknown parameters that are of scientific interest, which have to be estimated from noisy measurements of the dynamic system. Generally, there is no closed-form solution for nonlinear DEs, and the likelihood surface for the parameter of interest is multi-modal and very sensitive to different parameter values. We propose a Bayesian framework for nonlinear DE systems. A flexible nonparametric function is used to represent the dynamic process such that expensive numerical solvers can be avoided. A sequential Monte Carlo algorithm in the annealing framework is proposed to conduct Bayesian inference for parameters in DEs. In our numerical experiments, we use examples of ordinary differential equations and delay differential equations to demonstrate the effectiveness of the proposed algorithm. We developed an R package that is available at https://github.com/shijiaw/smcDE. Supplementary files for this article are available online. |
| Databáze: | OpenAIRE |
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