Unintelligible to non-experts 

Like most maths articles on Wikipedia, this one is unintelligible to someone that does not already know the material.

Consider an intelligent programmer with a basic knowledge of maths who wants to get an ideal of what all the talk about Baysian Networks is about, and whether they should read more.  Well, they won't be any the wiser from this article.  I have a PhD in Comp Sci (but limited knowledge of this field) and I can only follow the sprinkler example with effort, so don't tell me that it is intelligible.

The topic is technical, and we certainly do not want journalistic waffle.  But an introductory example of showing how the joint probablilities for a simple two node example can be simplified would be a good start.  Then maybe somthing about independent nodes which is not even mentioned.  Etc. 

The goal of Wikipedia is not to demonstrate how clever Wikipedians are.