Chapter 5 - Decision Analysis Fundamentals

Abstract

This chapter introduces decision trees that are mathematically equivalent to influence diagrams, but which have difficulty representing large instances because their size grows exponentially with the number of variables. A decision tree contains two kinds of nodes: chance nodes representing random variables and decision nodes representing decisions to be made. A decision represents a set of mutually exclusive and exhaustive actions the decision maker can take. Each action is called an alternative in the decision. There is an edge emanating from a decision node for each alternative in the decision. The expected utility (EU) of a chance node is defined to be the expected value of the utilities associated with its outcomes. The process of determining these expected utilities is called solving the decision tree. The entire process of identifying the components of a problem, structuring the problem as a decision tree (or influence diagram), solving the decision tree (or influence diagram), performing sensitivity analysis, and possibly reiterating these steps is called decision analysis. The chapter also discusses influence diagrams, whose size only grows linearly with the number of variables. The chapter also introduces dynamic Bayesian networks and influence diagrams that model relationships among random variables that change over time.