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Conditional independences given:

  1. A ⊥ C | B ---------- A and C are independent given B
  2. D ⊥ B | A, C
  3. E ⊥ C, D | A
  4. E ⊥ D | A

and I need to use this information for decomposing the full joint probability P(A, B, C, D, E).

My poor understanding leads me to

P(A, B, C, D, E) = P(B)P(A|B)P(C|B)P(E|A)P(D|A)

However, it does not seem to be correct, as 2. and 3. are just ignored by the answer.

Please kindly shed me some light on the question.

Thank you very much.

  • 0
    Just to clarify; what does E ⊥ C, D | A mean? D is independent of what?2011-04-28
  • 0
    @Stijn, I am not sure but I think it means E and C&D are independent given A.2011-04-28

2 Answers 2