Lecture 09 - Bayes Theorem

Lecture 09 - Bayes Theorem - Lecture 9 DADSS Decision...

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1 Lecture 9 Decision Analysis Bayes’ Theorem DADSS

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2 Administrative Details Homework Assignment 4 Due Homework Assignment 5 Distributed Midterm #1 is on March 1 st  at 6:00 PM Grading scheme Overview (subjects, question types) Review Sessions TBA on Blackboard Questions from last class?
3 Information and Value To this point, we have seen that… Information (often) has value How much value information has depends on: Whether we change our decisions What we know at the outset Prior or Initial Beliefs The degree of “illumination” provided by the information Stated differently, information is valued depending on  how much uncertainty is left facing the decision maker How can we quantify this?

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4 Acquiring Information Posterior Beliefs “Revised” Beliefs Bayes Theorem Posterior Beliefs Represent  Probabilities  Conditional  on  New Information Prior Beliefs Initial Information New Information Did you change your decision?
5 Common Questions How much should new information  change our initial beliefs? How much additional information should  we acquire? At what cost? How much information would be  required to change our decision? How much value should we place on  additional information?

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6 Introductory Concepts Prior Probabilities P(Sun), unconditional on other information (“base rate”) Joint Probabilities “Sun” is the expert’s forecast of the weather P(Sun  AND  “Sun”): The probability that both the forecast and  actual weather were sunny Conditional Probability P(“Sun” | Sun): The probability that  given  a sunny day, that the  forecast will be sunny Posterior Probability P(Sun | “Sun”): The probability that  given  a sunny forecast, that  the day will in fact be sunny Joint = Prior × Conditional P(Sun  AND  “Sun”) = P(Sun) × P(“Sun” | Sun) P(“Sun”|Sun) = P(Sun  AND  “Sun”) / P(Sun)       …simple math
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This note was uploaded on 09/20/2010 for the course SDS 88223 taught by Professor Fischbeck during the Spring '10 term at Carnegie Mellon.

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Lecture 09 - Bayes Theorem - Lecture 9 DADSS Decision...

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