Recently, I began to study Bayesian network models. It is of much interest. But I have figured out that every text book or any other paper about Bayesian network models does not contain comprehensive definition of messages.
I wish I can have one.
p.s. : If you may offer me a precise (preferably mathematical) definition of messages, I would appreciate that very very much.
It is not really a standard definition/vocabulary term. Typically, we refer to message-passing as the process of propagating probabilities across the network from node to node. These probabilities originate from the evidence that certain nodes have been instantiated in some way and are filtered via various conditional probabilities as the result of the dependencies in the model. Messages that travel through the network are usually of two forms: diagnostic and predictive. Children propagate diagnostic support to their parents (bottom-up) and parents provide predictive support to their children (top-down).
Now thats a layman's answer. There are precise heuristics for compiling these messages before delivering to other nodes. They are typically a product of the evidence gathered at the sending node from all its neighbouring nodes.