General Instruction
• Submit unzipped files in the Dropbox folder via BeachBoard (Not email or in class).
1. Consider Figure 1, and implement a program to answer the query ) 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. However, you have to implement a simulation program to answer (c).
(a) (8 points) Show
(b) (16 points) Show the transition probability matrix Q ∈ R4×4 where qij = transition probability from Si to Sj in Figure 2.
(c) (20 points) Show the probability of the query
(d) Please follow the output format. (Fix precisions using "0:.nf".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
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S2
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S3
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S4
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Part C. The probability for the query
P(C|-s,w) = <..., ...
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.
