Evaluating Influence Diagrams

TLDR

An influence diagram is a graphical model that represents uncertain variables, decisions, and their probabilistic dependencies, providing an intuitive yet precise framework for decision makers and experts to formulate problems and store information computationally. The authors develop an algorithm to evaluate any well‑formed influence diagram and compute the optimal decision policy. The algorithm evaluates influence diagrams directly, enabling model modifications to be made and re‑evaluated within the same formulation. Because the diagram can be analyzed directly, there is no need for alternative representations, the analysis remains in the decision maker's perspective, and sensitivity and value‑of‑information questions are naturally and easily addressed.

Abstract

An influence diagram is a graphical structure for modeling uncertain variables and decisions and explicitly revealing probabilistic dependence and the flow of information. It is an intuitive framework in which to formulate problems as perceived by decision makers and to incorporate the knowledge of experts. At the same time, it is a precise description of information that can be stored and manipulated by a computer. We develop an algorithm that can evaluate any well-formed influence diagram and determine the optimal policy for its decisions. Since the diagram can be analyzed directly, there is no need to construct other representations such as a decision tree. As a result, the analysis can be performed using the decision maker's perspective on the problem. Questions of sensitivity and the value of information are natural and easily posed. Modifications to the model suggested by such analyses can be made directly to the problem formulation, and then evaluated directly.