Related to belief networks, Please could you let me know the approach There are three computers indexed by i 2 f1; 2; 3g. Computer i can send a message in one timestep to computer j if Cij = 1, otherwise Cij = 0. There is a fault in the network and the task is to nd out some information about the communication matrix C (C is not necessarily symmetric). To do this, Thomas, the engineer, will run some tests that reveal whether or not computer i can send a message to computer j in t timesteps, t 2 f1; 2g. This is expressed as Cij(t), with Cij(1) Cij . For example, he might know that C13(2) = 1, meaning that according to his test, a message sent from computer 1 will arrive at
computer 3 in at most 2 timesteps. Note that this message could go via di erent routes { it might go directly from 1 to 3 in one timestep, or indirectly from 1 to 2 and then from 2 to 3, or both. You may assume Cii = 1. A priori Thomas thinks there is a 10 per cent probability that Cij = 1, i 6= j, and assumes that each such connection is independent of the rest. Given the test information C = fC12(2) = 1;C23(2) = 0g,
compute the a posteriori probability vector
[p(C12 = 1jC); p(C13 = 1jC); p(C23 = 1jC); p(C32 = 1jC); p(C21 = 1jC); p(C31 = 1jC)]