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← 11-14 Bayes_Rule_Diagram

11-14 Bayes_Rule_Diagram

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Showing Revision 3 created 11/02/2015 by Udacity Robot.

  1. What we really said that we had a situation where
  2. the prior P(C), a test with a certain sensitivity (Pos|C), and a certain specificity (Neg|¬C).
  3. When you receive, say, a positive test result, what you do is,
  4. you take your prior P(C) you multiply in the probability of this test result, given C,
  5. and you multiply in the probability of the test result given (Neg|¬C).
  6. So, this is your branch for the consideration that you have cancer.
  7. This is your branch for the consideration you have no cancer.
  8. When you're done with this, you arrive at a number
  9. that now combines the cancer hypothesis with the test result.
  10. Look for the cancer hypothesis and the not cancer hypothesis.
  11. Now, what you do, you add those up and then normally don't add up to one.
  12. You get a certain quantity which happens to be the total probability
  13. that the test is what it was, in this case positive.
  14. And all you do next is divide or normalize this thing over here by
  15. the sum over here and the same on the right side.
  16. The divider is the same for both cases because this is your cancer branch, your non-cancer branch,
  17. but this score does not depend on the cancer variable anymore.
  18. What you now get out is the desired posterior probability,
  19. and those add up to 1 if you did everything correct, as shown over here.
  20. This is the algorithm for Bayes Rule.