Diagnostic Strategies in the Probabilistic Causal Model

Abstract

In the probabilistic causal model described in the last chapter, symbolic causal knowledge and numeric probabilistic knowledge are integrated in a coherent and formal fashion. The relative likelihood L(D _I , M ⁺) was developed to evaluate the plausibility of hypothesis D _I given M ⁺, and was shown to be appropriate for identifying the Bayesian optimal diagnostic hypothesis. Recall that earlier, in Chapter 3, we defined the solution for a diagnostic problem to be the set of all irredundant covers of a given M ⁺. One difficulty concerning this definition is how to further disambiguate these alternatives (in some problems the number of irredundant covers of the given M ⁺ may be fairly large). The relative likelihood measure may be used to overcome this difficulty if we redefine the problem solution as the hypothesis with the highest relative likelihood value, i.e., the most probable one.

“But if probability is a measure of the importance of our state of ignorance, it must change its value whenever we add new knowledge. And so it does.”

Thornton C. Fry

Probability and Its Engineering Uses