Description
1. Consider Figure 1 (notice that some of the probabilities are different with the figure
in the textbook), and implement a program to answer the query P~ (C|¬s, w) by using
MCMC sampling. The program should generate 1, 000, 000 samples to estimate the
probability. To answer (a) and (b), you can prepare the answers with scratch paper and
print-out them (hard coding is fine). However, you are asked to implement a simulation
program to answer (c). Please use the filename mcmc.py. You may want to verify your
estimated probability with the one computed by using bayes.jar.
(a) (8 points) Show P~ (C|¬s, r), P~ (C|¬s, ¬r), P~ (R|c, ¬s, w), P~ (R|¬c, ¬s, w).
(b) (16 points) Show the transition probability matrix Q ∈ R
4×4 where
qij = transition probability from Si to Sj
in Figure 2.
(c) (20 points) Show the probability of the query P~ (C|¬s, w)
(d) Please follow the output format. (Fix precisions using “{:.4f}”.format)
Part A. The sampling probabilities
P(C|-s,r) = <…, …>
P(C|-s,-r) = <…, …>
P(R|c,-s,w) = <…, …>
P(R|-c,-s,w) = <…, …>
Part B. The transition probability matrix
S1 S2 S3 S4
S1 . . . .
S2 . . . .
S3 . . . .
S4 . . . .
Part C. The probability for the query
P(C|-s,w) = <…, …>
CECS 451 Assignment 9 – Page 2 of 2
Figure 1: A multiply connected network with conditional probability tables. Note that the
probabilities are slightly different than the lecture notes and the text book example.
Figure 2: Possible states diagram
