L09: Car Buyer Example Joe is going to buy a used car, which could be good with probability 0.8 or a lemon with probability 0.2. Joe's profit will be $60 if the car is good, and $-100 if it is bad. Before buying the car he has the option of having one test or two tests done on it. The first test costs $9, and both together cost $13. The first test has a 90% chance of returning positive if the car is good, and a 40% chance if it's a lemon. If the first test returns positive, then the second test has a 88.89% chance of returning positive if the car is good, and a 33.33% chance if it's a lemon. If the first test returns negative, then the second test has a 100% chance of returning positive if the car is good, and a 44.44% chance if it's a lemon. How to make the decisions: whether to do the tests, and whether to buy the car.

The Model: Decision Graph Random nodes Condition (C): {good, lemon}; First Test (F); Second Test (S): {not done, positive, negative} Decision Nodes Do Tests (T): {none, first, both}; Buy It (B): {buy don’t buy} Utility Nodes U: costs of tests; V: Profits

The Model: Decision Graph Probability Distributions for random variables P(C): P(S|F, C, T) P(F|C, T)

The Model: Decision Graph Utility functions for utility nodes U(T) V(C, B)

Analysis with Netica Finding optimal polices with Netica: Compile network and check “table” of decision nodes Best decision regarding Tests: none

Best decision regarding Buy: No test: Buy First test: Buy if positive Both test: Buy if both positive Impossible scenarios crossed out

Analysis with Netica Netica can also compute expected values for different scenario: Just set the node values, and let Netica do the rest. T=none B=buy: Expected Value: 28 B=don’t buy Expected Value: 0

Analysis with Netica T=first F=positive (0.8) B=buy 35 (best second decision) B=don’t buy -9 F=negative (0.2) B=buy -45 B=don’t buy -9 (best second decision)