Using the Sneezing example (without the leak probability) of Unit # 7, compute the joint probability distribution of Sneezing, Allergy, Cold and Dust. Use this joint distribution to compute P(Sneezing | ~Allergy, Cold, ~Dust), P(Sneezing | ~Allergy, ~Cold, Dust) and P(Sneezing | Allergy, ~Cold, ~Dust). Are these computed conditional probabilities consistent with the expert provided conditional probabilities (Noisy-Or terms)? [Note: It is important to remember that when we write Noisy-Or terms, we commonly write P(S | A) or P(S | D) but it is implicit that we mean P(S | A, ~C, ~D) or P(S | ~A, ~C, D), respectively.]

Further assume that our expert has also provided the probability P(Sneezing | Allergy, Dust) = 0.65. Use the Recursive Noisy-Or approach to first recompute the conditional probability table of Sneezing and then compute the joint distribution of all four variables. Use this joint distribution to compute P(Sneezing | ~Allergy, Cold, ~Dust), P(Sneezing | ~Allergy, ~Cold, Dust), P(Sneezing | Allergy, ~Cold, ~Dust) and P(Sneezing | Allergy, ~Cold, Dust). Are these computed conditional probabilities consistent with the expert provided conditional probabilities?

Using the CAST logic example of Unit # 8 (first assume baseline probability as 0 and then as 0.3), compute the conditional probability table of X and the joint distribution of A, B, C and X. Is it possible to relate different g and h values to corresponding conditional probabilities, such as hx|a to P(X | A, ~B, ~C) or P(X | A, B, C) or P(X | A, ~B, C) or P(X | A, B, ~C), and so on. [Note: There is no known answer to this question, so you have to work really hard to see if a relationship exist between different g and h values and the corresponding computed conditional probabilities.]

Problem 2 (Due on November 7, 2009)

Develop a Bayesian network of a real world situation. Feel free to use any knowledge acquisition techniques (Noisy-Or, CAST logic) if you find it hard to specify all the conditional probability values in your BN. You can work in a group of 2 to develop and analyze your BN.

## CSE655: Probabilistic Reasoning

## Assignment # 3

## Date: October 25, 2009

Problem 1 (Due on November 4, 2009)Problem 2 (Due on November 7, 2009)