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Unformatted text preview: a. Assume that the doctor is also informed about the frequencies of h 1 , h 2 , h 3 . In other words, he knows the prior probabilities q j := P ( h j ), j = 1, 2, 3. As we know, the MAP hypothesis has the best chance to hit the target hypothesis. How large is f in case q 1 = q 2 = q 3 = 1/3? b. Due to an epidemy of h 3 , the frequencies (priors) suddenly changed into q 1 = q 2 = 0.1 and q 3 = 0.8. What is f now, if the MAP hypothesis is used as preliminary diagnosis? c. Can you make a correct preliminary diagnosis with probability 0.45, even if you are completely ignorant of prior probabilities? (Hint: A purely random guess would succeed with probability 0.33. Using the table of the P ( D i | h j ), it should be possible to improve upon this trivial strategy.) Compare the result to (a)....
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- Winter '10
- Machine Learning