2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/133912Symbolic 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.8 pages, 1 figure; http://cse.ucdavis.edu/~cmg/compmech/pubs/hrct.htmMachine LearningInformation TheoryChaotic Dynamicstext