Sinossi
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
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