1 / 6

Decision Making Cycle

Decision Making Cycle. Define Decision. Bayes Theorem. Collect/ Capture Data. Assess Uncertainty in Data. Determine Value of Reducing Uncertainty. Make Decision. Gather Additional Data. N. Y. Derivation of Bayes Theorem. C is a universe of outcomes such that P(C) = 1. B. A. C.

lotta
Download Presentation

Decision Making Cycle

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Decision Making Cycle Define Decision Bayes Theorem Collect/Capture Data Assess Uncertaintyin Data DetermineValue of Reducing Uncertainty Make Decision Gather AdditionalData N Y

  2. Derivation of Bayes Theorem C is a universe of outcomes such that P(C) = 1. B A C P(A) = Area A / Area CP(A|B) = P(A and B) / P(B), so by substitution, P(B|A) = P(B and A) / P(A)P(A|B) * P(B) = P(B|A) * P(A)P(A|B) = [ P(B|A) * P(A) ] / P(B) Bayes Theorem

  3. Bayes Theorem (Cont.) Outcome 1 P(A) + P(A) = 1,P(B) + P(B) = 1P(B) = P(B|A) * P(A) +P(B|A) * P(A)P(A|B) = [P(B|A) * P(A)] [P(B|A) * P(A) + P(B|A) * P(A)] B A B Outcome 2 Outcome 3 B A B Outcome 4 Bayes TheoremRestated

  4. Example .63.18.09.02.03.05 No Redesign Original Design Meets Cust. Req. .7 Minor Redesign .2 .9 .1 Major Redesign Original Design Does NOT Meet Cust. Req. No Redesign .2 .1 .3 Minor Redesign .5 Major Redesign 1

  5. Bayesian Estimation • In general, there are two types of approaches to estimation of parameters: • Frequentist - Estimates an unknown parameter based only on observed data and an adopted model - Characterized by scientific objectivity • Bayesian - Estimates an unknown parameter by appropriately combining prior intuition or knowledge with information from observed data - Characterized by subjective nature of prior opinion • Each approach is valid when applied under specific circumstances.Neither approach will uniformly dominate the other

  6. Bayes’ Theorem Exercise Many combat aircraft carry air-to-air missiles. A warning light will notify the pilot if the missile is defective. If the missile is defective an alternative missile may be used or the mission may need to be aborted. The missile may or may not be defective when the warning light is on. Given the warning light indicates a bad missile - what is the probability the missile is really defective? Approach: Define Event A as the missile is a dud. Define Event B as the warning device signals the missile is a dud. From product specs it is known that: P(A) = .0001 i.e., one missile in 10000 is a dud. P(B|A) = .9998 i.e., the probability of the avionics hardware and software detecting and reporting a defective missile is .9998 P(B|not A) = .002 i.e., probability of a false warning is .002

More Related