Question

Consider the pairwise Markov network,

p(x) = Ⲫ(X1,x2) Ⲫ(X2,x3) Ⲫ(X3,x4) Ⲫ(X4,x1)
Express in terms of d) the following:
p(X1IX2, X4), p(x2|x1, X3), p(x3|x2, X4), p(x4|x1, X3)

Answer 1

To express the given probabilities in terms of the provided pairwise Markov network, we need to consider the conditional probabilities and the given edges between the variables. Here is the expression for each probability.

Step-by-step explanation:

To express the given probabilities in terms of the provided pairwise Markov network, we need to consider the conditional probabilities and the given edges between the variables. Here is the expression for each probability:

1. p(X1|X2, X4) = Ⲫ(X1,X2,X4) / Ⲫ(X2,X4)
2. p(X2|X1, X3) = Ⲫ(X1,X2,X3) / Ⲫ(X1,X3)
3. p(X3|X2, X4) = Ⲫ(X2,X3,X4) / Ⲫ(X2,X4)
4. p(X4|X1, X3) = Ⲫ(X1,X3,X4) / Ⲫ(X1,X3)