How Random is a Coin Toss? Bayesian Inference and the Symbolic Dynamics of Deterministic Chaos

Details How Random is a Coin Toss? Bayesian Inference and the Symbolic Dynamics of Deterministic Chaos How Random is a Coin Toss? Bayesian Inference and the Symbolic Dynamics of Deterministic Chaos

2006-11-13

arxiv.org/abs/cs/0611054v1

Computer Science

Learning

8 pages, 1 figure; http://cse.ucdavis.edu/~cmg/compmech/pubs/hrct.htm

Scientific paper

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.

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