An Odds Ratio Based Inference Engine

Expert systems applications that involve uncertain inference can be represented by a multidimensional contingency table. These tables offer a general approach to inferring with uncertain evidence, because they can embody any form of association between any number of pieces of evidence and conclusions. (Simpler models may be required, however, if the number of pieces of evidence bearing on a conclusion is large.) This paper presents a method of using these tables to make un­ certain inferences without assumptions of conditional independence among pieces of evidence or heuristic combining rules. As evidence is accumu­ lated, new joint probabilities are calculated so as to maintain any dependencies among the pieces of evidence that are found in the contin­ gency table. The new conditional probability of the conclusion is then calculated directly from these new joint probabilities and the conditional probabilities in the contingency table. INTRODUCTION The information for expert systems applications that involve uncertain inference can be represented by a multidimensional contingency table which has a dimension for each piece of evidence and a dimension for the conclusion. Suppose, for example, that each piece of evidence and the conclusion can have two states, true (or present) and false (or absent). Then each cell in the contingency table contains the joint probability for the associated states of each piece of evidence and the conclusion. Unfortunately, with this scheme a contingency table for 19 pieces of evidence and one conclusion will have over a million cells. As Shortliffe and Buchanan (1975) point out, it is not possible to estimate such large numbers of probabilities satisfactorily. Thus, attention has focused on ways .to avoid estimating such large numbers of joint probabilities.