L20_ECE4001_Fall_2009

L20_ECE4001_Fall_2009 - Lecture 20 Bayesian Decision Making...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
J. Stevenson Kenney © 2009 1 Lecture 20 Bayesian Decision Making And Cost Benefit Analysis November 5, 10, 2009
Background image of page 1

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

View Full DocumentRight Arrow Icon
J. Stevenson Kenney © 2009 2 Using probability for decision making Probability trees Decision tree methods Can combine with engineering economy Chapter 9 of Hyman
Background image of page 2
J. Stevenson Kenney © 2009 3 Probability Trees Graphical representations consists of: 1. Branches: (straight lines) 2. Event or chance nodes (circles) C D E C D E A B
Background image of page 3

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

View Full DocumentRight Arrow Icon
J. Stevenson Kenney © 2009 4 Evaluating Risk • A = Circuit works • B = Circuit fails • If P(A) > P(B), choose A • If P(A) < P(B), choose B • Note that P(A) + P(B) = 1 A B • When confronted with multiple options, one may need to assess the risk of each option • Simple example: P(A) P(B)
Background image of page 4
J. Stevenson Kenney © 2009 5 Dependencies • A and B must be occur before C or D can be chosen A B C D C D P(A) P(B) P(D|A) P(C|A) P(D|B) P(C|B) Note: P(A) + P(B) = 1 P(C|A) + P(D|A) = 1 P(C|B) + P(D|B) = 1
Background image of page 5

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

View Full DocumentRight Arrow Icon
J. Stevenson Kenney © 2009 6 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
Background image of page 6
J. Stevenson Kenney © 2009 7 “Inverting” the Decision Tree • We may need to prepare for later decisions before making earlier decisions – Planning resource allocation – Purchasing materials – Scheduling services • To do this, we must “invert” the decision tree using Bayes’ theorem
Background image of page 7

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

View Full DocumentRight Arrow Icon
J. Stevenson Kenney © 2009 8 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
Background image of page 8
J. Stevenson Kenney © 2009 9 Bayes’ Theorem ( | ) the probability of event given event has occurred may be calculated using: () (| ) ) where, a set of mutually exclusive and mutually exhaustive events: ( ) 1 a d ii i i i i PA B A B PAPB A PB AP A B = = == = ependent event that occurs only if event occurs ( ) the probability of event occuring ( | ) the probability of event given event has occurred ( ) the probability of event occuring i A PA A PB A B A B = = =
Background image of page 9

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

View Full DocumentRight Arrow Icon
J. Stevenson Kenney © 2009 10 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 Forward Tree is “reactive” (little planning) Reverse Tree is “responsive” (much planning)
Background image of page 10
J. Stevenson Kenney © 2009
Background image of page 11

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

View Full DocumentRight Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 33

L20_ECE4001_Fall_2009 - Lecture 20 Bayesian Decision Making...

This preview shows document pages 1 - 12. Sign up to view the full document.

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