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Lecture3 Modelling Decision Processes

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Kodok Ngorex
Kodok Ngorex
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Modelling Decision Processes Reading: Chapter 4 ,[object Object],[object Object],You cannot get to where you are going if you don’t know where you are! Today’s philosophical point
Defining the Problem and Its Structure ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Problem Definition Errors ,[object Object],[object Object],[object Object],[object Object]
E.G. Problem Statement ,[object Object],[object Object],[object Object],[object Object],Current Desired objective +
Problem Scope ,[object Object],[object Object],[object Object]
Problem Structure ,[object Object],[object Object],[object Object],[object Object],[object Object]
Problem Structure (cont.) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Structuring Tools ,[object Object],Decision Objective Uncertainty Decision Uncertainty Decision tree: another diagram that models choices and uncertainties and can be extended to include multiple, sequential decisions
Decision Tree Example ,[object Object],[object Object],Win £5000 Lose wager Make large profit Lose most of stake Lose/gain nothing 10:1 bet on a horse Invest in stock Do nothing Horse wins Horse loses Significant rise Stocks fall Minor profit/loss Steady change http:// www.psychwww.com/mtsite/dectree.html
Exponential growth of DT’s
Common Decision Structures ,[object Object],[object Object],[object Object],[object Object]
Decision Models ,[object Object],[object Object],[object Object]
Model Classification Examples ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Conceptual Models ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Types of Probability ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Lets look at a Decision Tree again 0.5 Lets keep the maths easy by using p=0.5 for all uncertainties 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 P=0.25 P=0.25 P=0.5 P=0.25 P=0.25 P=0.25 P=0.25 A A1 B1 B2 B ALL uncertainties for events = 1
How Are Probabilities Generated? ,[object Object],[object Object],[object Object],[object Object]
Forecasting Probabilities? ,[object Object],[object Object],[object Object]
Calculating Odds in a D/Tree Bet on team A Bet against team A Team A wins Team A loses Team A loses Team A wins £Xx -£X £Y -£Y P(Team A wins)=Y/(X+Y) see text for detail, pg 125/6
Decomposing Complex Probabilities ,[object Object],[object Object]
Conditional and Total Probabilities Severe winter P(B)=0.7 Moderate winter 1 - P(B)=0.3 Sales > 1000 P(A|B) Sales >= 1000 1 - P(A|B) Sales > 1000 P(A|B`) Sales <= 1000 1 - P(A|B`) 0.8 0.2 0.5 0.5 P(A)=P(A|B) * P(B) = P(A|B`) * P(B) = 0.71
Calibration ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Sensitivity Analysis ,[object Object],[object Object],[object Object]
Value Analysis ,[object Object],[object Object],[object Object]
Key Points ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Lecture3 Modelling Decision Processes

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  • 16. Lets look at a Decision Tree again 0.5 Lets keep the maths easy by using p=0.5 for all uncertainties 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 P=0.25 P=0.25 P=0.5 P=0.25 P=0.25 P=0.25 P=0.25 A A1 B1 B2 B ALL uncertainties for events = 1
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  • 19. Calculating Odds in a D/Tree Bet on team A Bet against team A Team A wins Team A loses Team A loses Team A wins £Xx -£X £Y -£Y P(Team A wins)=Y/(X+Y) see text for detail, pg 125/6
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  • 21. Conditional and Total Probabilities Severe winter P(B)=0.7 Moderate winter 1 - P(B)=0.3 Sales > 1000 P(A|B) Sales >= 1000 1 - P(A|B) Sales > 1000 P(A|B`) Sales <= 1000 1 - P(A|B`) 0.8 0.2 0.5 0.5 P(A)=P(A|B) * P(B) = P(A|B`) * P(B) = 0.71
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