1. Part II − Application to Markov Structures

2. A Motivating Example ✕✕✕✕✕✕✕✕

3. Conditional Mutual Independence

4. Example 1

5. Example 2

6. Example 3

7. ____________________________ _________

8. Full Conditional Mutual Independence (FCMI)

10. Notations

18. Illustration of Im(K)

29. The Implication Problem

41. Markov Random Field

42. Graph Theory Terminologies

46. Global Markov Property

50. FCMIs Specified by a MRF

55. Type I and Type II Atoms

60. A Graph-Theoretic Analog

63. Markov Chain

64. Special Properties of a Markov Chain

68. Construction of Information Diagram

73. Nonnegativity of µ*

76. A Formal Justification