Problem_Session_4

Problem_Session_4 - MS&E 252 - Problem Session 4...

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06/17/10 MS&E 252 - Problem Session 4 1 MS&E 252 Decision Analysis I Problem Session 4
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06/17/10 MS&E 252 - Problem Session 4 2 Announcements Case Study Groups Start forming groups of 4 within your problem session. Email your TA by Monday, Nov. 5 th , with the names of your team members.
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06/17/10 MS&E 252 - Problem Session 4 3 Announcements: More Importantly Homework Performance - Probability assignment: were you that sure? - Someone assigned a zero probability and guess what, he was wrong - How we handle direct questions on homework - We will tell you to assign probabilities - We can only help with conceptual questions Optimal Strategy: Represent your beliefs… … But first, know your beliefs
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06/17/10 MS&E 252 - Problem Session 4 4 On Today’s Menu Probability Review The Rules of Arrow Flipping The Five Rules of Actional Thought Five Rules Problems Questions?
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06/17/10 MS&E 252 - Problem Session 4 5 Three Doors One door leads to a treasure. The other two lead to nothing. A wizard lets you pick a door. Which door do you pick? A B C
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06/17/10 MS&E 252 - Problem Session 4 6 Three Doors Then, he proceeds to open one of the doors you did not pick. The door he opened had no treasure. He now gives you a final choice: You can change your decision and open the last remaining door. Or, you can stick to your present decision. What should you do? What is your intuition?
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06/17/10 MS&E 252 - Problem Session 4 7 D1 D2 D3 1/3 1/3 1/3 “D2” “D3” 1/2 1/2 “D1” “D3” 0 1 “D1” “D2” 0 1 1/6 1/3 1/6 0 0 1/3 Treasure in Wizard eliminates Assume you picked D1 Three Doors – Draw the Tree
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06/17/10 MS&E 252 - Problem Session 4 8 “D2” “D3” 1/2 1/2 D1 D3 1/3 2/3 D1 D2 1/3 2/3 1/6 1/3 1/3 1/6 Wizard eliminates In both cases, the probability of treasure being in the other door is higher (other than D1). Treasure in Three Doors – Flip the Tree
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06/17/10 MS&E 252 - Problem Session 4 9 On Today’s Menu Probability Review The Rules of Arrow Flipping The Five Rules of Actional Thought Five Rules Problems Questions?
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06/17/10 MS&E 252 - Problem Session 4 10 “Add arrows wherever you want, provided you don’t create a cycle; A cycle made by more than 3 nodes is also not allowed.” A B C We can only flip arrows according to certain rules. RULE #1 X X
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06/17/10 MS&E 252 - Problem Session 4 11 “You can flip an arrow between A and B if and only if A and B are conditioned on the same state of information.” We can only flip arrows according to certain rules. RULE #2 In other words, any other node (here, C and D) which points to A also points to B. A B D C ? *Tip* – Draw a box around A and B
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06/17/10 MS&E 252 - Problem Session 4 12 “You cannot remove any arrows arbitrarily.” We can only flip arrows according to certain rules. RULE #3 A B
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06/17/10 MS&E 252 - Problem Session 4 13 An example of recognizing irrelevance from diagrams.
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Problem_Session_4 - MS&E 252 - Problem Session 4...

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