Description
1. Consider the following problem which was discussed in class:
Suppose that we have a patient who was just tested for a particular disease and
the test came out positive. We know that one in every thousand people has this
disease. We also know that the test is not reliable: it has a false positive rate of 2%
and a false negative rate of 5%. Our goal is then to assess our belief in the patient
having the disease given that the test came out positive. If we let the propositional
variable D stand for the patient has the disease, and the propositional variable T
stand for the test came out positive, our goal is then to compute P r(D|T).
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You may also recall being surprised that P r(D|T) ≈ 0.045. The goal of this question is then
to identify conditions under which this probability will be no less than .30. You will need to
find the answer to this by constructing a Bayesian Network and using the sensitivity analysis
engine of SamIam. You need to turn in test.net and a report that contains the following
information:
• Your complete Bayesian network (Structure and CPTs) in test.net file.
• A constraint on each of the following, which is sufficient to ensure that P r(D|T) ≥ 0.3:
The prior probability of having the disease, the false positive for the test, and the false
negative for the test. Screenshot the results from SamIam and attach the pictures in the
report.
Hint: you need to choose an algorithm like sheony-shafer to run the sensitivity analysis.
2. Consider the following scenario:
When Sambot goes home at night, he wants to know if his family is home before
he tries the doors. (Perhaps the most convenient door to enter is double locked
when nobody is home). Often when Sambot’s wife leaves the house she turns on
an outdoor light. However, she sometimes turns on this light if she is expecting a
guest. Also, Sambot’s family has a dog. When nobody is home, the dog is put in
the back yard. The same is true if the dog has bowel trouble. Finally, if the dog
is in the backyard, Sambot will probably hear her barking, but sometimes he can
be confused by other dogs barking. Sambot is equipped with two sensors: a lightsensor for detecting outdoor lights and a sound-sensor for detecting the barking of
dogs(s). Both of these sensors are not completely reliable and can break. Moreover,
they both require Sambot’s battery to be in good condition.
Your task is to build a belief network that Sambot will use to reason about the above situation
using the modeling and inference tool SamIam. Specifically, given sensory input, Sambot
needs to compute his beliefs in various events: whether his family is home, whether any of
his sensors are broken, whether the dog is in the backyard, and whether it has bowel trouble.
You need to proceed as follows:
(a) Decide on the set of variables and their values. These variables and values must
match those in the given data file sambot.dat.
(b) Construct the causal structure.
(c) Learn the network CPTs using the EM algorithm and the data file (sambot.dat)
available from the class homepage. Your initial network should have uniform parameters.
You need to turn in sambot.net and a report that contains the following information:
• The most likely instantiation of all variables given that Sambot has sensed the lights to
be on, but has sensed no bark. Explain how you obtained this answer (for partial credit
in case you get the wrong answer). Screenshot the results from SamIam and attach the
pictures in the report.
• The most likely instantiation of the sensors given that the family is home and no guests
are expected. Explain how you obtained this answer (for partial credit in case you get
the wrong answer). Screenshot the results from SamIam and attach the pictures in the
report.
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• The smallest set of variables Z in your network such that the two sensors are independent
given Z. Justify your answer based on d-separation.
• The type of network you constructed: tree, polytree (singly-connected network), or
multiply-connected network.
Hint: you need to choose an algorithm like sheony-shafer to run the EM algorithm.
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