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Christopher C Strelioff1, James P Crutchfield

  • 1Center for Computational Science and Engineering and Physics Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA. streliof@uiuc.edu

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Summary
This summary is machine-generated.

This study introduces a new Bayesian inference method for analyzing noisy time series data using symbolic dynamics. The approach effectively infers generating partitions and Markov chain models from complex dynamical systems.

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Area of Science:

  • Dynamical Systems and Chaos Theory
  • Statistical Inference
  • Information Theory

Background:

  • Time series analysis often involves finite, noisy data.
  • Symbolic dynamics offers a method for simplifying complex time series.
  • Bayesian inference provides a robust framework for statistical modeling.

Purpose of the Study:

  • To adapt Bayesian inference for symbolic dynamics analysis.
  • To reconcile maximum-entropy partitions with Bayesian model selection.
  • To develop a method for inferring generating partitions and Markov models from noisy time series.

Main Methods:

  • Applied Bayesian inference to symbolic dynamics.
  • Utilized two-step optimization: maximum-entropy partition and minimum-entropy model selection.
  • Employed binary partitioning of time series data.
  • Analyzed data from logistic, Henon, Rössler, and Lorenz systems with added noise.

Main Results:

  • Demonstrated successful reconciliation of Kolmogorov's maximum-entropy partition with Bayesian model selection.
  • Showcased the inference of effectively generating partitions.
  • Successfully inferred kth-order Markov chain models for the symbolic data.
  • Validated the method on various chaotic attractors with dynamical noise.

Conclusions:

  • The proposed Bayesian approach provides a powerful tool for analyzing finite, noisy time series.
  • This method enables robust inference of underlying dynamical system properties through symbolic representation.
  • The dual optimization strategy effectively captures essential information from complex data.