Qualitative Reasoning of Bayesian Belief Using Meta-knowledge

Ordering composite hypotheses in a Bayesian network based on its associated a posteriori probabilities can be exponentially hard. This paper discusses a qualitative reasoning approach which reduces the computational complexity of deriving a partial ordering of composite hypotheses. Such a reasoning makes use of the meta-knowledge about the causal relationships among individual hypotheses to deduce qualitative conclusions about the ordering of local composite hypotheses. By doing so, we can employ "divide and conquer" strategy to derive the global ordering of the composite hypotheses from a set of local ordering in which consistencies are guaranteed. We view the contribution of this research is on the integration of qualitative reasoning with the use of local computations to find not only the most likely composite hypotheses, but also the partial ordering of the composite hypotheses. I. Introduction A Bayesian network [Pearl 86,87] is a graphical representation of probabilistic knowledge about the causal relationships among a set of variables (propositions) in an expert system. Each of these variables accounts for a set of possible outcomes, each of which is a hypothesis. A permutation of the outcomes accounted for by different variables is referred to as a composite hypothesis. For example, if the causal relationships among heatstroke (one kind of heat illness) and its pathological states (such as body temperature , level of consciousness, etc.) are represented in terms of a Bayesian network for use in computer aided medical diagnosis, one possible composite hypothesis can be: not heatstroke and high body temperature and low level of consciousness.