| Publication type: | Article in scientific journal |
| Type of review: | Peer review (publication) |
| Title: | Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation |
| Authors: | Albert, Carlo Ulzega, Simone Stoop, Ruedi |
| DOI: | 10.1103/PhysRevE.93.043313 |
| Published in: | Physical Review E |
| Volume(Issue): | 93 |
| Issue: | 4 |
| Issue Date: | 2016 |
| Publisher / Ed. Institution: | American Physical Society |
| ISSN: | 2470-0045 2470-0053 |
| Language: | English |
| Subjects: | Computer Science - Data Structures and Algorithms; Statistics - Computation |
| Subject (DDC): | 003: Systems 510: Mathematics |
| Abstract: | Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model, for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact and very efficient approach for generating posterior parameter distributions, for stochastic differential equation models calibrated to measured time-series. The algorithm is inspired by re-interpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for 1D problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable. |
| URI: | https://digitalcollection.zhaw.ch/handle/11475/14773 |
| Fulltext version: | Published version |
| License (according to publishing contract): | Licence according to publishing contract |
| Departement: | Life Sciences and Facility Management |
| Organisational Unit: | Institute of Computational Life Sciences (ICLS) |
| Appears in collections: | Publikationen Life Sciences und Facility Management |
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Albert, C., Ulzega, S., & Stoop, R. (2016). Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation. Physical Review E, 93(4). https://doi.org/10.1103/PhysRevE.93.043313
Albert, C., Ulzega, S. and Stoop, R. (2016) ‘Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation’, Physical Review E, 93(4). Available at: https://doi.org/10.1103/PhysRevE.93.043313.
C. Albert, S. Ulzega, and R. Stoop, “Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation,” Physical Review E, vol. 93, no. 4, 2016, doi: 10.1103/PhysRevE.93.043313.
ALBERT, Carlo, Simone ULZEGA und Ruedi STOOP, 2016. Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation. Physical Review E. 2016. Bd. 93, Nr. 4. DOI 10.1103/PhysRevE.93.043313
Albert, Carlo, Simone Ulzega, and Ruedi Stoop. 2016. “Boosting Bayesian Parameter Inference of Nonlinear Stochastic Differential Equation Models by Hamiltonian Scale Separation.” Physical Review E 93 (4). https://doi.org/10.1103/PhysRevE.93.043313.
Albert, Carlo, et al. “Boosting Bayesian Parameter Inference of Nonlinear Stochastic Differential Equation Models by Hamiltonian Scale Separation.” Physical Review E, vol. 93, no. 4, 2016, https://doi.org/10.1103/PhysRevE.93.043313.
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