Problem 3
The Chest Clinic Bayesian network (see the following figure) concerns the diagnosis of lung disease (tuberculosis, lung cancer, or both, or neither). In this model a visit to Asia is assumed to increase the probability of tuberculosis.
x - Positive X-ray
d = Dyspnea (Shortness of breath)
e = Either Tuberculosis or Lung Cancer
t = Tuberculosis
l = Lung Cancer
b = Bronchitis
a - Visited Asia
s = Smoker
Figure 2: BN model of chest clinic
3.1 Factorize the joint distribution based on this BN model.
3.2 Use the Bayes' ball algorithm or the AMDD algorithm to validate or invalidate the following statements:
tuberculosis ∑ smoking | shortness of breath
lung cancer ∑ bronchitis | smoking
visit to Asia ∑ smoking | lung cancer
visit to Asia ∑ smoking | lung cancer, shortness of breath
3.3 Assume that all nodes are binary, i.e., True or False. The conditional probabilities are given below:
P(a = T) = 0.01, P(s = T) = 0.5, P(t = T|a = T) = 0.05, P(t = T|a = F) = 0.01, P(l = T|s = T) = 0.1, P(l = T|s = F) = 0.01, P(b = T|S = T) = 0.6, P(b = T|S = F) = 0.3, P(x = T|e = T) = 0.98, P(x = T|e = F) = 0.05, P(d = T|e = T, b = T) = 0.9, P(d = T|e = T, b = F) = 0.7, P(d = T|e = F, b = T) = 0.8, P(d = T|e = F, b = F) = 0.1, and P(e = T|t, l) = 0 only if both t and l are F's, and 1 otherwise.
Calculate the values for P(x = T), P(x = T|t = F), P(t = T|X = F) and P(t = T|x = F, d = T).