bayes rule

# bayes rule - Bayes Rule P A j | = P Aj P B | j P A P B | i...

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Bayes’ Rule: 1 () *( ) ) jj j N ii i PA PB PA PB = | Α |Β = | Α It might look ugly, but it is very useful. The only thing is you have to correctly set-up the events. For example, the Ai’s are a partition of your sample space. Most Bayes problems will have 2 partitions of the sample space. Therefore you have to choose the one partition that you are using based on the above formula. Example from Class: We have “Disease D” that affects 15% of the population. Suppose the test for Disease D turns out + 95% of the time you actually have Disease D. Suppose further that the test for Disease D turns out – 90% of the time you do not have Disease D. There are 2 natural partitions in this problem. One is do you or do you not have Disease D. The other is did you test positive or negative. Let D be the event that you have Disease D. Let O be the event that you test positive. In relation to the Bayes’ formula above, would D and be the partition (i.e. would D and act as the Ai’s) or would O and be the partition?

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bayes rule - Bayes Rule P A j | = P Aj P B | j P A P B | i...

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