How Random is a Coin Toss? Bayesian Inference and the Symbolic Dynamics of Deterministic Chaos
<|reference_start|>How Random is a Coin Toss? Bayesian Inference and the Symbolic Dynamics of Deterministic Chaos: Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a coarse-grained description of the behavior that accurately describes the invariant properties of an underlying chaotic attractor. In particular, measures of the rate of information production--the topological and metric entropy rates--can be estimated from the outputs of Markov or generating partitions. Here we develop Bayesian inference for k-th order Markov chains as a method to finding generating partitions and estimating entropy rates from finite samples of discretized data produced by coarse-grained dynamical systems.<|reference_end|>
@article{strelioff2006how,
    title={How Random is a Coin Toss? Bayesian Inference and the Symbolic Dynamics
  of Deterministic Chaos},
    author={Christopher C. Strelioff and James P. Crutchfield},
    journal={arXiv preprint arXiv:cs/0611054},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0611054},
    primaryClass={cs.LG cs.IT math.IT nlin.CD}
}