Physics – Data Analysis – Statistics and Probability
Scientific paper
2011-10-06
Phys. Rev. E 85 (2), 026705 (2012)
Physics
Data Analysis, Statistics and Probability
18 pages, 2 figures
Scientific paper
10.1103/PhysRevE.85.026705
Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic dynamics in time. Recently techniques for the estimation of the corresponding stochastic differential equations from measured data have been introduced. This contribution develops a framework for the estimation of the functions and their respective (Bayesian posterior) confidence regions based on likelihood estimators. In succession approximations are introduced that significantly improve the efficiency of the estimation procedure. While being consistent with standard approaches to the problem this contribution solves important problems concerning the applicability and the accuracy of estimated parameters.
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