Problem
Consider the network, but now assume that we make Z a slightly noisy exclusive or of its parents. That is, with some small probability q, Z is chosen uniformly at random regardless of the values of X and Y, and with probability 1 - q, Z is the exclusive or of X and Y. Analyze the transitions between states in the Gibbs chain for this network, with the evidence z1, and particularly the expected time required to transition between different regions.