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Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation
- Publication Year :
- 2016
-
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.<br />15 pages, 8 figures
- Subjects :
- FOS: Computer and information sciences
Mathematical optimization
3104 Condensed Matter Physics
Stochastic modelling
Bayesian probability
Posterior probability
Inference
01 natural sciences
Statistics - Computation
Hybrid Monte Carlo
010104 statistics & probability
Stochastic differential equation
0103 physical sciences
Computer Science - Data Structures and Algorithms
Data Structures and Algorithms (cs.DS)
3109 Statistical and Nonlinear Physics
Statistical physics
0101 mathematics
2613 Statistics and Probability
010306 general physics
Computation (stat.CO)
Mathematics
10194 Institute of Neuroinformatics
510: Mathematik
Statistical mechanics
Bayesian statistics
003: Systeme
570 Life sciences
biology
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....3b35d4b3cf6b3f57d3564bf4cbf5c532