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

Publication Date

6-2019

Document Type

Article

Organizational Units

College of Arts Humanities and Social Sciences, Psychology

Keywords

Complexity, Markov process, Lempel–Ziv, Predictability

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.

Copyright Date

1-30-2019

Copyright Statement / License for Reuse

All Rights Reserved
All Rights Reserved.

Publication Statement

Copyright is held by the American Educational Research Association. User is responsible for all copyright compliance. This article was originally published as:

Vegetabile, B. G., Stout-Oswald, S. A., Davis, E. P., Baram, T. Z., & Stern, H. S. (2019). Estimating the entropy rate of finite Markov chains with application to behavior studies. Journal of Educational and Behavioral Statistics, 44(3), 282-308. https://doi.org/10.3102/1076998618822540

Rights Holder

American Educational Research Association

Provenance

Received from CHORUS

Language

English (eng)

Publication Title

Journal of Educational and Behavioral Statistics

Volume

44

Issue

3

First Page

282

Last Page

308

ISSN

1935-1054

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