Before making an unsecured loan to an individual a bank orders a report on the applicantĂ˘â‚¬â„˘s credit history. To justify making the loan, the bank must find the applicantĂ˘â‚¬â„˘s credit record to be satisfactory. Describe the bankĂ˘â‚¬â„˘s decision. What are the bankĂ˘â‚¬â„˘s objectives? What risk does the bank face? What role does the credit report play? Using PrecisionTree, create an influence diagram of this situation. (Hint: Your influence diagram should include chance nodes for a credit report and for eventual default. Also, Precision Tree can convert influence diagrams into decision tress and this can be helpful in checking your work. See Problem 3.26 for instructions on conversion.) Finally, be sure to specify everything (decisions, chance events, objectives) in your model clearly enough to pass the clarity test.
PrecisionTree will convert any influence diagram into the corresponding decision tree with the click of a button. This provides an excellent opportunity to explore the meaning of arrows in an influence diagram because you can easily see the effect of adding or deleting an arrow in the corresponding decision tree. Because we are only concerned with the structural effect of arrows, we will not input numerical values.
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a. Construct the influence diagram in Exercise 3.11(a) in PrecisionTree. Convert the influence diagram to a decision tree by right-clicking on the influence diagramĂ˘â‚¬â„˘s name (straddling cells A1 and B1) to pull up a menu, then choose Model and finally click on Convert To Decision Tree.
b. Add an arrow from the Ă˘â‚¬Ĺ“WeatherĂ˘â‚¬Âť chance node to the Ă˘â‚¬Ĺ“PartyĂ˘â‚¬Âť decision node and convert the influence diagram into a decision tree. Why would the decision tree change in this way?
c. Construct the influence diagram in Exercise 3.11(b) in PrecisionTree. Convert the influence diagram to a decision tree. How would the decision tree change if the arrow started at the Ă˘â‚¬Ĺ“PartyĂ˘â‚¬Âť decision node and went into the Ă˘â‚¬Ĺ“ForecastĂ˘â‚¬Âť node? What if, in addition, the arrow started at the Ă˘â‚¬Ĺ“ForecastĂ˘â‚¬Âť chance node and went into the Ă˘â‚¬Ĺ“WeatherĂ˘â‚¬Âť chance node?