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Birkhäuser

Nonlinear Dynamics and Statistics

  • Book
  • © 2001

Overview

Editors:
  1. Alistair I. Mees

    1. Centre for Applied Dynamics and Optimization, University of Western Australia, Perth, Australia

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xxii
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  3. Fundamentals

    1. Front Matter

      Pages 167-167
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    2. An Introduction to Monte Carlo Methods for Bayesian Data Analysis

      • Christophe Andrieu, Arnaud Doucet, William J. Fitzgerald
      Pages 169-217

    3. Constrained Randomization of Time Series for Nonlinearity Tests

      • Thomas Schreiber, Andreas Schmitz
      Pages 219-232

    4. Removing the Noise from Chaos Plus Noise

      • Steven P. Lalley
      Pages 233-244

    5. Embedding Theorems, Scaling Structures, and Determinism in Time Series

      • Colleen D. Cutler
      Pages 245-265

    6. Consistent Estimation of a Dynamical Map

      • Andrew Nobel
      Pages 267-280

    7. Extracting Dynamical Behavior via Markov Models

      • Gary Froyland
      Pages 281-321

    8. Formulas for the Eckmann-Ruelle Matrix

      • Timothy D. Sauer
      Pages 323-336

  4. Methods and Applications

    1. Front Matter

      Pages 337-337
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    2. Noise and Nonlinearity in an Ecological System

      • Paul A. Dixon, Maria J. Milicich, George Sugihara
      Pages 339-364

    3. Cluster-Weighted Modeling: Probabilistic Time Series Prediction, Characterization, and Synthesis

      • Bernd Schoner, Neil Gershenfeld
      Pages 365-385

    4. Data Compression, Dynamics, and Stationarity

      • Matthew B. Kennel, Alistair I. Mees
      Pages 387-412
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Keywords

About this book

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.

Editors and Affiliations

  • Centre for Applied Dynamics and Optimization, University of Western Australia, Perth, Australia

    Alistair I. Mees

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