Non-sequential recursive pair substitutions and numerical entropy estimates in symbolic dynamical systems

TL;DR

This paper evaluates a non-sequential recursive pair substitution method for estimating entropy in ergodic sources, comparing it with classical techniques across various dynamical systems with different statistical properties.

Contribution

It introduces and tests a novel recursive pair substitution method for entropy estimation, supported by rigorous mathematical results and extensive numerical experiments.

Findings

The method performs well across different systems.

It provides accurate entropy estimates compared to classical methods.

The approach is supported by theoretical analysis.

Abstract

We numerically test the method of non-sequential recursive pair substitutions to estimate the entropy of an ergodic source. We compare its performance with other classical methods to estimate the entropy (empirical frequencies, return times, Lyapunov exponent). We considered as a benchmark for the methods several systems with different statistical properties: renewal processes, dynamical systems provided and not provided with a Markov partition, slow or fast decay of correlations. Most experiments are supported by rigorous mathematical results, which are explained in the paper.