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Estimating the Entropy Rate of Finite Markov Chains With Application to Behavior Studies

Author

Listed:
  • Brian G. Vegetabile

    (University of California-Irvine)

  • Stephanie A. Stout-Oswald

    (University of Denver)

  • Elysia Poggi Davis

    (University of Denver University of California-Irvine)

  • Tallie Z. Baram
  • Hal S. Stern

    (University of California-Irvine)

Abstract

Predictability of behavior is an important characteristic in many fields including biology, medicine, marketing, and education. When a sequence of actions performed by an individual can be modeled as a stationary time-homogeneous Markov chain the predictability of the individual’s behavior can be quantified by the entropy rate of the process. This article compares three estimators of the entropy rate of finite Markov processes. The first two methods directly estimate the entropy rate through estimates of the transition matrix and stationary distribution of the process. The third method is related to the sliding-window Lempel–Ziv compression algorithm. The methods are compared via a simulation study and in the context of a study of interactions between mothers and their children.

Suggested Citation

  • Brian G. Vegetabile & Stephanie A. Stout-Oswald & Elysia Poggi Davis & Tallie Z. Baram & Hal S. Stern, 2019. "Estimating the Entropy Rate of Finite Markov Chains With Application to Behavior Studies," Journal of Educational and Behavioral Statistics, , vol. 44(3), pages 282-308, June.
    • Handle: RePEc:sae:jedbes:v:44:y:2019:i:3:p:282-308
    DOI: 10.3102/1076998618822540
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