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Markov Structures

  • Raymond W. Yeung
Chapter
  • 598 Downloads
Part of the Information Technology: Transmission, Processing and Storage book series (PSTE)

Abstract

We have proved in Section 6.5 that if X1X2X3X4 forms a Markov chain, the I-Measure μ* always vanishes on the five atoms
$$\eqalign{ & {\widetilde X_1} \cap \widetilde X_2^c \cap {\widetilde X_3} \cap \widetilde X_4^c \cr & {\widetilde X_1} \cap \widetilde X_2^c \cap {\widetilde X_3} \cap \widetilde X_4^{} \cr & {\widetilde X_1} \cap \widetilde X_2^c \cap \widetilde X_3^c \cap {\widetilde X_4} \cr & {\widetilde X_1} \cap {\widetilde X_2} \cap \widetilde X_3^c \cap {\widetilde X_4} \cr & \widetilde X_1^c \cap {\widetilde X_2} \cap \widetilde X_3^c \cap {\widetilde X_4}. \cr} $$
(7.1)
Consequently, the I-Measure μ* is completely specified by the values of J.L* on the other ten nonempty atoms of F4, and the information diagram for four random variables forming a Markov chain can be displayed in two dimensions as in Figure 6.11.

Keywords

Markov Chain Markov Random Field Discrete Time Markov Chain Rectangular Lattice Basic Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Raymond W. Yeung
    • 1
  1. 1.The Chinese University of Hong KongHong Kong

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