Optimal instruments and models for noisy chaos.
Analysis of finite, noisy time series data leads to modern statistical inference methods. Here we adapt Bayesian inference for applied symbolic dynamics. We show that reconciling Kolmogorov's maximum-entropy partition with the methods of Bayesian model selection requires the use of two separate optimizations. First, instrument design produces a maximum-entropy symbolic representation of time series data. Second, Bayesian model comparison with a uniform prior selects a minimum-entropy model, with respect to the considered Markov chain orders, of the symbolic data. We illustrate these steps using a binary partition of time series data from the logistic and Henon maps as well as the Rössler and Lorenz attractors with dynamical noise. In each case we demonstrate the inference of effectively generating partitions and kth-order Markov chain models.
Strelioff
Christopher C
CC
Center for Computational Science and Engineering and Physics Department, University of California at Davis, One Shields Avenue, Davis, California 95616, USA. streliof@uiuc.edu
Crutchfield
James P
JP
D000465:Algorithms; D001499:Bayes Theorem; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D019277:Entropy; D004867:Equipment Design; D008390:Markov Chains; D015233:Models, Statistical; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated; D013269:Stochastic Processes