bayes rule

bayes rule - Bayes' Rule: P ( A j | ) = P( Aj ) * P( B | j...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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?
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

bayes rule - Bayes' Rule: P ( A j | ) = P( Aj ) * P( B | j...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online