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You are given three different Bayesian network structures (1, 2, 3), for three alarm system designs. Each system consists of 4 binary random variables (A, B, C, D). Each variable corresponds to an alarm condition in an assembly line in a factory, whose state can be either “ON” or “OFF”. Structures in image   Using the chain rule of probability for Bayes Nets, factor P(A,B,C,D) according to the independencies specified in the three structures above. What is the minimum number of parameters required to fully specify the distribution (i.e. to calculate P(A,B,C,D))? Hint: The chain rule of probability P(A,B) = p(A|B) p(B) for three variables: P(A,B,C) = P(A| B,C) P(B,C) = P(A|B,C) P(B|C) P(C) and in general to n variables: P(A1, A2, ..., An) = P(A1| A2, ..., An) P(A2| A3, ..., An) P(An-1|An) P(An)

You are given three different Bayesian network structures (1, 2, 3), for three alarm system designs. Each system consists of 4 binary random variables (A, B, C, D). Each variable corresponds to an alarm condition in an assembly line in a factory, whose state can be either “ON” or “OFF”. Structures in image   Using the chain rule of probability for Bayes Nets, factor P(A,B,C,D) according to the independencies specified in the three structures above. What is the minimum number of parameters required to fully specify the distribution (i.e. to calculate P(A,B,C,D))? Hint: The chain rule of probability P(A,B) = p(A|B) p(B) for three variables: P(A,B,C) = P(A| B,C) P(B,C) = P(A|B,C) P(B|C) P(C) and in general to n variables: P(A1, A2, ..., An) = P(A1| A2, ..., An) P(A2| A3, ..., An) P(An-1|An) P(An)

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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You are given three different Bayesian network structures (1, 2, 3), for three alarm system designs. Each system consists of 4 binary random variables (A, B, C, D). Each variable corresponds to an alarm condition in an assembly line in a factory, whose state can be either “ON” or “OFF”.

Structures in image

 

Using the chain rule of probability for Bayes Nets, factor P(A,B,C,D) according to the independencies specified in the three structures above. What is the minimum number of parameters required to fully specify the distribution (i.e. to calculate P(A,B,C,D))?

Hint: The chain rule of probability

  • P(A,B) = p(A|B) p(B)

for three variables:

  • P(A,B,C) = P(A| B,C) P(B,C) = P(A|B,C) P(B|C) P(C)

and in general to n variables:

  • P(A1, A2, ..., An) = P(A1| A2, ..., An) P(A2| A3, ..., An) P(An-1|An) P(An)

Structure 1 B Structure 2 B Structure 3
Transcribed Image Text:Structure 1 B Structure 2 B Structure 3
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