L21_ECE4001_Spring_2011 - Announcements Lecture 21 Bayesian...

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1 Slide #1 ECE 4001 L21 © 2011 T. Michaels Lecture 21 Bayesian Decision Making And Cost Benefit Analysis Slide #2 ECE 4001 L21 © 2011 T. Michaels Announcements HW6 due today HW7 due next Wednesday, 4/13 Report your stock choices on HW7 as requested Slide #3 ECE 4001 L21 © 2011 T. Michaels Using probability for decision making Use Bayes’ theorem with application to a series of events Decision tree methods Can combine with engineering economy Chapter 9 of Hyman Slide #4 ECE 4001 L21 © 2011 T. Michaels Bayes’ Theorem B B P A B A B P A A P A B A B P A B P A P B A P B A B A P i i i i i i i i i i i event of y probabilit the ) ( occurred has event given event of y probabilit the ) | ( event of y probabilit the ) ( occurs event if only occurs event that dependent a events exhaustive mutually and exclusive mutually of set a where, ) ( ) | ( ) ( ) | ( : using calculated be may occurred has event given event of y probabilit the ) | ( = = = = = = =
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2 Slide #5 ECE 4001 L21 © 2011 T. Michaels Probability Trees Graphical representations consists of: 1. Branches: (straight lines) 2. Event or chance nodes (circles) C D E C D E A B Slide #6 ECE 4001 L21 © 2011 T. Michaels Probability Tree Starting With Chance Node (A or B) C D E P(A) C D E A B P(B) P(C|A) P(D|A) P(E|A) P(C|B) P(D|B) P(E|B) P(A) + P(B) = 1 P(C|A) + P(D|A) + P(E|A) = 1 P(C|B) + P(D|B) + P(E|B) = 1 Slide #7 ECE 4001 L21 © 2011 T. Michaels Probability Tree Starting With Chance Node (C, D or E) A B P(C) C E P(A|C) P(B|C) D A B P(A|E) P(B|E) A B P(A|D) P(B|D) P(D) P(E) P(C) + P(D) + P(E) = 1 P(A|C) + P(B|C) = 1 P(A|D) + P(B|D) = 1 P(A|E) + P(B|E) = 1 Slide #8 ECE 4001 L21 © 2011 T. Michaels Probability Tree Starting With Chance Node (C, D or E) A B P(C) C E P(A|C) P(B|C) D A B P(A|E) P(B|E) A B P(A|D) P(B|D) P(D) P(E) C D E P(A) C D E A B P(B) P(C|A) P(D|A) P(E|A) P(C|B) P(D|B) P(E|B) Forward Probability Tree Reverse Probability Tree Use Bayes” theorem to invert probability trees
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3 Slide #9 ECE 4001 L21 © 2011 T. Michaels There is a plane crash. The plane crash may be located in the mountains, fields, or in the ocean. An initial search failed to locate the crash site. What is the probability that the crash site is located in the mountains? Region Prob. Located Prob. Finding Mountains 0.5 0.7 Fields 0.3 0.8 Ocean 0.2 0.1 Draw the probability tree starting with the region chance node Draw the probability tree starting with the find/lost chance node Slide #10 ECE 4001 L21 © 2011 T. Michaels Region Prob. Located Prob. Finding Mountains 0.5 0.7 Fields 0.3 0.8 Ocean 0.2 0.1 Mt. 0.5 Fields 0.3 Ocean 0.2 Find Lost Find Lost Find Lost 0.7 0.8 0.1 Starting Chance Node - Region 0.3 0.2 0.9 Slide #11 ECE 4001 L21 © 2011 T. Michaels Probability of finding crash site: P(Find) = P(Find|Mt) P(Mt) + P(Find|Fields) P(Fields) + P(Find|Ocean) P(Ocean) P(Find) = 0.7 (0.5) + 0.8 (0.3) + 0.1 (0.2) = 0.61 P(Lost) = 1 – P(Find) = 1 – 0.61 = 0.39 or P(Lost) = P(Lost|Mt) P(Mt) + P(Lost|Fields) P(Fields) + P(Lost|Ocean) P(Ocean)
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This note was uploaded on 04/18/2011 for the course ECE 4001 taught by Professor Frazier during the Spring '09 term at Georgia Institute of Technology.

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L21_ECE4001_Spring_2011 - Announcements Lecture 21 Bayesian...

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