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← 01ps-05 Bayes Rule

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Showing Revision 1 created 02/27/2012 by Amara Bot.

  1. I'm now going to quiz you on Bayes Rule.
  2. Say you own a house, and you know that the house might catch fire in your absence,
  3. but the probability of it catching fire--"f" over here--is small.
  4. It's a 10th of a percent--0.001.
  5. Let's say every afternoon you talk to your neighbor, and every afternoon
  6. you ask your neighbor, "Does my house burn?"
  7. Of course,you a little bit paranoid if you do this, but for the sake of the argument,
  8. let's just assume you do this every afternoon.
  9. This afternoon he comes back and says, "Yes, it burns," so B.
  10. You happen to know that the neighbor is not very truthful.
  11. In fact, every time you ask him a question,
  12. you know there is a 0.1 chance--a 10% chance--the neighbor will just produce a lie
  13. and a 0.9 chance the neighbor actually speaks the truth.
  14. So you ask him exactly one question--"Does my house burn?"
  15. He says, "Yes, it burns," but you know that the probability of this being a lie is 0.1.
  16. So in applying Bayes Rule I like to first compute the non-normalized posterior--p bar--
  17. bar now stands for non-normalized--of fire given the neighbor just called.
  18. The same for the opposite event of no fire given the neighbor just said, yes, it burns.
  19. After you've done this, I'd like you to compute the normalized values
  20. that have to add up to 1.
  21. Please enter all 4 values for this homework assignment.