Meyer R, Christensen N. Bayesian reconstruction of chaotic dynamical systems.
PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000;
62:3535-3542. [PMID:
11088853 DOI:
10.1103/physreve.62.3535]
[Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2000] [Revised: 05/23/2000] [Indexed: 05/23/2023]
Abstract
We present a Bayesian approach to the problem of determining parameters of nonlinear models from time series of noisy data. Recent approaches to this problem have been statistically flawed. By applying a Markov chain Monte Carlo algorithm, specifically the Gibbs sampler, we estimate the parameters of chaotic maps. A complete statistical analysis is presented, the Gibbs sampler method is described in detail, and example applications are presented.
Collapse