HW #8

Provide answers to the following questions. Submit your answers through blackboard in .pdf format.

1. Use the AIspace Bayesian Network applet to construct a Bayes net that corresponds to the naive Bayes classifier from the previous homework. Use your Bayes net to answer the following questions:
   • What is the probability that a patient with fever and no headache has pneumonia? What is the probability that the patient has the flu? What is the probability that the patient is healthy?
   • Our patient is unconscious, so can't tell us whether or not she has a headache. She does have a fever. What is the probabilities distribution over her health status?
   Include a screen-shot of your Bayes net with no observations and monitoring turned on for every node.

2. Consider the following xkcd comic:

   

   Assuming that the Bayesian statistician estimates the prior probability of a sun explosion to be 1/1,000,000,000,

   • what probability will he assign to the proposition that the sun has exploded after detector says YES.? What probability will he assign to the proposition that the sun has not exploded?
   • What is the expected utility (in dollars) of his $50 bet?

3. Consider the following probability distribution:

   P(X = red) = .2
   P(X = green) = .1
   P(X = blue) = .7
   
   • Given this distribution, what is the likelihood of the following data set?

     < red, green, blue, blue, red >

   • What is the distribution with the maximum likelihood for this data set? What is the likelihood of the data set for that distribution?