[Solved] CECS451 Assignment 9

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).

• (8 points) Show
• (16 points) Show the transition probability matrix Q ∈ R^4×4 where q_ij = transition probability from S_i to S_j in Figure 2.
• (20 points) Show the probability of the query
• 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	.	.	.	.
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