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Exam SS 18
I found this on an old exam:
Problem 1.3 (Medical Bayesian Network 2)
Both Malaria and Meningitis can cause a fever, which can be measured by checking for a 12pt
12min high body temperature. We consider the following random variables for a given patient:
• M al: The patient has malaria.
• Men: The patient has meningitis.
• HBT: The patient has a high body temperature.
• F: The patient has a fever.
- Draw the corresponding Bayesian network for the above data using the algorithm
presented in the lecture, assuming the variable order M al, Men, HBT, F. Explain
rigorously(!) the exact criterion for whether to insert an arrow between two nodes. - Which arrows are causal and which are diagnostic? Which order of variables would
be better suited for constructing the network?
The resulting bayes net was the same as the one from our exercises and this makes me question two things:
→ Why is Fever only influenced by HBT, given the information above? It is possible to have a fever without a high body temperature. Hence, I would have drawn edges from Mal & Men to fever as well.
→ Also there is no answer to the question which order of variables would be better suited (1.3.2). In my opinion the fever should come before the hbt, because it causes a HBT and Mal & Men can cause Fever. This way my bayes net would now have the edges from Mal & Men to Fever as well but there will be only an edge from fever to hbt as fever can cause a hbt. Mal & Men only cause fever. But in the (official) solution on the exam sheet it would make no difference.
In the real world? I have no idea what a fever is if not a high body temperature, but:
So in the context of the exercise, it is assumed that a high body temperature is (necessary and) sufficient to diagnose a fever. Consequently, Men and Mal only influence fever via a high body temperature. Whether that’s medically accurate, I have no idea, I’d guess not 
Yes. Because the arrow from HBT to F is diagnostic rather than causal, and in general we prefer causal arrows over diagnostic ones.
It is very unlikely, but as I understood it, possible (I googled it :-D).
This sentence would be so great to just have in an assignment like that. I understand that this is kind of common sense, but there are so many exceptions - especially in medicine - and how are we to know that this is assumed?
So nevertheless, I feel like the question is formulated very generically. If such a question appeared in Tuesday’s exam I would write down my assumptions next to the network if there is no information (for example → I am assuming that a fever does not necessarily need the patient to have a hbt).
In your solution, this would not make any difference in the network, so I do not see a benefit except the change from diagnostic to causal edge.
When in doubt, ask! We’re there for a reason, after all
I consider that a benefit