| Chris C. Strelioff Center for Complex Systems Research and Department of Physics University of Illinois at Urbana-Champaign Urbana, IL 61801 and Center for Computational Science and Engineering University of California at Davis Davis, CA 95616 |
James P. Crutchfield |
ABSTRACT: Analysis of finite, noisy time series data leads necessarily 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 Rossler and Lorenz attractors with dynamical noise. In each case we demonstrate the inference of effectively generating partitions and k-th order Markov chain models.