Part II −
Application to Markov Structures
A Motivating Example
✕ ✕ ✕ ✕
Conditional Mutual
Independence
Example 1
Example 2
Example 3
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Full Conditional Mutual
Independence
(FCMI)
Notations
Notations
Notations
Notations
Illustration of Im(K)
Illustration of Im(K)
The Implication Problem
The Implication Problem
The Implication Problem
The Implication Problem
The Implication Problem
Markov Random Field
Graph Theory Terminologies
Graph Theory Terminologies
Graph Theory Terminologies
Graph Theory Terminologies
Global Markov Property
Global Markov Property
Global Markov Property
Global Markov Property
FCMIs Specified by a MRF
FCMIs Specified by a MRF
FCMIs Specified by a MRF
FCMIs Specified by a MRF
FCMIs Specified by a MRF
Type I and Type II Atoms
Type I and Type II Atoms
Type I and Type II Atoms
Type I and Type II Atoms
A Graph-Theoretic Analog
Markov Chain
Special Properties of a Markov
Chain
Special Properties of a Markov
Chain
Special Properties of a Markov
Chain
Construction of Information
Diagram
Construction of Information
Diagram
Construction of Information
Diagram
Construction of Information
Diagram
Construction of Information
Diagram
Nonnegativity of µ*
Nonnegativity of µ*
Nonnegativity of µ*
A Formal Justification