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The Entropy as a State Function01:14

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Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
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Transfer entropy as a log-likelihood ratio.

Lionel Barnett1, Terry Bossomaier

  • 1Sackler Centre for Consciousness Science, School of Informatics, University of Sussex, Brighton, United Kingdom. l.c.barnett@sussex.ac.uk

Physical Review Letters
|October 4, 2012
PubMed
Summary
This summary is machine-generated.

Transfer entropy quantifies directed information flow between processes. A new statistical test consistently estimates transfer entropy, linking it to Granger causality for complex systems analysis.

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Area of Science:

  • Information Theory
  • Complex Systems Analysis
  • Statistical Inference

Background:

  • Transfer entropy is a popular measure for analyzing directed information transfer in complex stochastic systems.
  • Applications span neurosciences, ecology, climatology, and econometrics.

Purpose of the Study:

  • To develop a consistent statistical estimator for transfer entropy.
  • To establish a theoretical framework connecting transfer entropy with Granger causality.

Main Methods:

  • Utilizing log-likelihood ratio test statistics for hypothesis testing.
  • Analyzing a broad class of predictive models.
  • Establishing asymptotic distributions for estimators.

Main Results:

  • The log-likelihood ratio test statistic is a consistent estimator for transfer entropy.
  • An asymptotic χ2 distribution is established for the estimator in the general case.
  • The method does not require explicit models for finite Markov chains.

Conclusions:

  • This work provides a robust statistical foundation for transfer entropy estimation.
  • It generalizes existing results and establishes a fundamental link between information transfer and Wiener-Granger causality.