Synopses & Reviews
Recently, a great deal of progress has been made in the modeling and understanding of processes with nonlinear dynamics, even when only time series data are available. Modern reconstruction theory deals with creating nonlinear dynamical models from data and is at the heart of this improved understanding. Most of the work has been done by dynamicists, but for the subject to reach maturity, statisticians and signal processing engineers need to provide input both to the theory and to the practice. The book brings together different approaches to nonlinear time series analysis in order to begin a synthesis that will lead to better theory and practice in all the related areas. This book describes the state of the art in nonlinear dynamical reconstruction theory. The chapters are based upon a workshop held at the Isaac Newton Institute, Cambridge University, UK, in late 1998. The book's chapters present theory and methods topics by leading researchers in applied and theoretical nonlinear dynamics, statistics, probability, and systems theory. Features and topics: * disentangling uncertainty and error: the predictability of nonlinear systems * achieving good nonlinear models * delay reconstructions: dynamics vs. statistics * introduction to Monte Carlo Methods for Bayesian Data Analysis * latest results in extracting dynamical behavior via Markov Models * data compression, dynamics and stationarity Professionals, researchers, and advanced graduates in nonlinear dynamics, probability, optimization, and systems theory will find the book a useful resource and guide to current developments in the subject.
Synopsis
Recently, a great deal of progress has been made in the modeling and understanding of processes with nonlinear dynamics, even when only time series data are available. This is a state-of-the-art survey of the theory and methods used for nonlinear time series analysis. The chapters are written by leading researchers in nonlinear dynamics, statistics, probability, optimization, and systems theory and cover both theory and applications. Professionals, researchers, and students working in these fields will find this to be an indispensable resource.
Synopsis
All models are lies. "The Earth orbits the sun in an ellipse with the sun at one focus" is false, but accurate enough for almost all purposes. This book describes the current state of the art of telling useful lies about time-varying systems in the real world. Specifically, it is about trying to "understand" (that is, tell useful lies about) dynamical systems directly from observa tions, either because they are too complex to model in the conventional way or because they are simply ill-understood. B(: cause it overlaps with conventional time-series analysis, building mod els of nonlinear dynamical systems directly from data has been seen by some observers as a somewhat ill-informed attempt to reinvent time-series analysis. The truth is distinctly less trivial. It is surely impossible, except in a few special cases, to re-create Newton's astonishing feat of writing a short equation that is an excellent description of real-world phenomena. Real systems are connected to the rest of the world; they are noisy, non stationary, and have high-dimensional dynamics; even when the dynamics contains lower-dimensional attractors there is almost never a coordinate system available in which these at tractors have a conventionally simple description."
Synopsis
This book describes the state of the art in nonlinear dynamical reconstruction theory. The chapters are based upon a workshop held at the Isaac Newton Institute, Cambridge University, UK, in late 1998. The book's chapters present theory and methods topics by leading researchers in applied and theoretical nonlinear dynamics, statistics, probability, and systems theory. Features and topics: * disentangling uncertainty and error: the predictability of nonlinear systems * achieving good nonlinear models * delay reconstructions: dynamics vs. statistics * introduction to Monte Carlo Methods for Bayesian Data Analysis * latest results in extracting dynamical behavior via Markov Models * data compression, dynamics and stationarity Professionals, researchers, and advanced graduates in nonlinear dynamics, probability, optimization, and systems theory will find the book a useful resource and guide to current developments in the subject.
Table of Contents
Section I: Issues in Reconstructing Dynamics; Challenges in Modeling Nonlinear Systems: A Worked Example; Disentangling Uncertainty and Error: On the Predictability of Nonlinear Systems; Achieving Good Nonlinear Models: Keep it Simple, Vary the Embedding, and Get the Dynamics Right; Delay Reconstruction: Dynamics vs. Statistics; Some Remarks on the Statistical Modelling of Chaotic Systems; The Identification and Estimation of Nonlinear Stochastic Systems; Section II: Fundamentals; An Introduction to Monte Carlo Methods for Bayesian Data Analysis; Contrained Randomization of Time Series For Nonlinearity Tests; Removing the Noise from Chaos Plus Noise; Embedding Theorems, Scaling Structures, and Determinism in Time Series; Consistent Estimation of a Dynamical Map; Extracting Dynamical Behaviour via Markov Models; Formulas for the Eckmann-Ruelle Matrix; Section III: Methods and Applications; Noise and Nonlinearity in an Ecological System; Cluster-Weighted Modeling: Probabilistic Time Series Prediction, Characterization and Synthesis; Data Compression, Dynamics and Stationarity; Analyzing Nonlinear Dynamical Systems with Nonparametric Regression; Optimization of Embedding Parameters for Prediction of Seizure Onset with Mutual Information; Detection of a Nonlinear Oscillator Underlying Experimental Time Series: The Sunspot Cycle