If I have an undirected graph (markov chain) with 4 variables:
X1 - X2 - X3 - X4
Each variable can take 2 values: 0 or 1.
And I have transition matrices going from X1 to X2, X2 to X3, and X3 to X4:
X1 to X2:
0.1 0.7
0.8 0.3
(eg: if X1=0, then there's 0.1 probability that X2 will be 0, 0.7 probability that X2 will be 1. If X1=1, 0.8 prob that X2 will be 0, 0.3 probability that X2 will be 1)
X2 to X3
0.5 0.1
0.1 0.5
X3 to X4
0.9 0.3
0.1 0.3
Using the "forward pass" and "backward pass" junction tree algorithm, find the marginal probability distributions for each variable.
A step-by-step numerical solution is appreciated. Thanks!!!!
