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An improved estimator of Shannon entropy with applications to systems with memory

Author

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  • De Gregorio, Juan
  • Sánchez, David
  • Toral, Raúl

Abstract

We investigate the memory properties of discrete sequences built upon a finite number of states. We find that the block entropy can reliably determine the memory for systems modeled as Markov chains of arbitrary finite order. Further, we provide an entropy estimator that remarkably gives accurate results when correlations are present. To illustrate our findings, we calculate the memory of daily precipitation series at different locations. Our results are in agreement with existing methods being at the same time valid in the undersampled regime and independent of model selection.

Suggested Citation

  • De Gregorio, Juan & Sánchez, David & Toral, Raúl, 2022. "An improved estimator of Shannon entropy with applications to systems with memory," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p1:s0960077922009766
    DOI: 10.1016/j.chaos.2022.112797
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    References listed on IDEAS

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    1. Mayzelis, Z.A. & Apostolov, S.S. & Melnyk, S.S. & Usatenko, O.V. & Yampol’skii, V.A., 2007. "Additive N-step Markov chains as prototype model of symbolic stochastic dynamical systems with long-range correlations," Chaos, Solitons & Fractals, Elsevier, vol. 34(1), pages 112-128.
    2. Philipp Singer & Denis Helic & Behnam Taraghi & Markus Strohmaier, 2014. "Detecting Memory and Structure in Human Navigation Patterns Using Markov Chain Models of Varying Order," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-21, July.
    3. Michael Seifert & André Gohr & Marc Strickert & Ivo Grosse, 2012. "Parsimonious Higher-Order Hidden Markov Models for Improved Array-CGH Analysis with Applications to Arabidopsis thaliana," PLOS Computational Biology, Public Library of Science, vol. 8(1), pages 1-15, January.
    4. Yulmetyev, R.M. & Demin, S.A. & Panischev, O. Yu. & Hänggi, Peter & Timashev, S.F. & Vstovsky, G.V., 2006. "Regular and stochastic behavior of Parkinsonian pathological tremor signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 655-678.
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    Cited by:

    1. Piga, Angelo & Font-Pomarol, Lluc & Sales-Pardo, Marta & Guimerà, Roger, 2024. "Bayesian estimation of information-theoretic metrics for sparsely sampled distributions," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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