Probabilistic causal reasoning in intelligent systems
Albert Hoang · 1993
In this thesis I investigate some methods of probabilistic causal reasoning in the framework of influence Diagrams (IDs). Probabilistic causal reasoning here refers to a process of deriving new probabilistic causal statements using some procedures or predefined rules of inference upon a known set of statements describing some probabilistic causal relationships among variables of interest. A probabilistic causal statement is a kind of probability inequality of the form $p(A\mid B,{\bf X}) - \rm p(A\mid B) \ge (\le,=)0$ where A,B,X are variables under consideration. Thus probabilistic causal reasoning is a kind of probabilistic reasoning with a particular type of probability inequality which describes causal relationships among variables in a way similar to human thinking without resort to point probabilities. For a general ID, I first explore the implications of the use of Arc Reversal and Variable Reduction transformations as a means to infer the causal relationship among some variables of interest, and then develop a strategy to guide this inference process. Unfortunately there is some difficulty in determining what the known statements should be for the inference process to always five a relatively good answer. However for a kind of IDs that are singly connected, this difficulty does not appear as I show that in this setting, there is a set of rules of inference that operates well on a particular type of prespecified causal statements.