I had an interesting time yesterday writing a rule set in order to demonstrate that Bayesian analytics can be combined with rule processing in an entirely natural fashion. Armed with an understanding of how a rules engine works, I also believe that it is entirely possible for a Rules Engine to implement and apply Bayes theorem in an efficient manner. I wrote the rule set for a Java-based rule engine called Jess, so please note this is not a BizTalk-related post.
My reason for writing the rule set was to counter some statements published on the Complex Event Processing Blog site, including references to a 20-year old academic paper that appears to claim, incorrectly, that rules engines cannot efficiently handle the concept of uncertainty. Bayes theory is one way of handling dependencies amongst uncertain beliefs (i.e., calculating the probability (and changes to probability) of the accuracy of hypotheses based on uncertain beliefs and evidence). Another approach to handling uncertainty is to employ 'fuzzy logic', which I found myself demonstrating to a client (using MS BRE) just last week. But that's another story...
If you are interested in this rather obscure discussion, please read on at http://geekswithblogs.net/cyoung/archive/2007/08/27/114988.aspx