Entropy methods in decision analysis.

摘要

This dissertation explores the application of information theory to the assignment of probability and utility values when incomplete information is available about the decision maker's beliefs and preferences.; The first part of the dissertation deals with the application of the maximum entropy principle to the assignment of univariate and joint probability distributions in decision analysis. The focus is on maximum entropy distributions given probability assessments rather than moments and correlation coefficients that are more difficult to elicit in practice. Chapter 3 provides a new graphical solution to the maximum entropy formulation given fractile constraints, and chapter 4 provides new approximations to the maximum entropy joint distribution using lower order probability assessments.; The second part of the dissertation presents an analogy between probability and utility, and discusses the application of information theory to the elicitation and assignment of utility values in decision analysis. Chapter 5 presents an optimal question selection algorithm for utility elicitation. The algorithm uses questions that require binary responses that are easier to provide than numeric values and uses coding principles to ask the minimal expected number of questions. Chapter 6 introduces an analogy between probability and utility through the notion of a utility density function, which is the derivative of a normalized utility function. The analogy leads to a maximum entropy utility principle to assign utility values based on incomplete preference information. Chapter 7 introduces an analogy between joint cumulative distributions and a class of multiattribute utility functions. The analysis leads to the notion of utility inference and Bayes' rule for utility. Chapter 8 introduces new dual concepts that result from interchanging probability functions and utility functions, such as the aspiration equivalent (the dual to the certain equivalent), the dual decision problem, utility dominance relationships, and directions for further research.