A common problem with filters is fact that they are a one-size-fits all solution to SPAM. The rules are concrete and only change based on input from updates from Anti-spam service.
SPAM changes too quickly to make that method effective. Additionally, what is SPAM to you may not be to someone else. That is where Bayesian filters come in.
They are very effective at eliminating SPAM and have very low false-positive rates for their users.
Bayesian filters are based on Bayesian logic, a branch of logic named for Thomas Bayes, an eighteenth century Mathematician.
This type of logic applies to decision making by determining probability of a certain event based on history of past events.
Using this as a model seemed a logical step for SPAM filtering. If you can predict what SPAM will look like now based on what is has looked like in past, you are halfway to solution.
To finish solving problem, Bayesian filters were developed to be dynamic and continue to be effective as SPAM changes.
Bayesian filters are content based. They look for characteristics in each email that you receive and calculate probability of it actually being SPAM.
These characteristics are generally words in content and header file information that each email contains. They can also include common SPAM HTML code, word pairs, phrases, and location of a phrase in body of email.
Typical words in SPAM would be "Free" and "Win", while "humility" would probably not appear. The filter begins with a 50% neutral score for email, and then adds points for SPAM characteristics.
Likewise, deductions are made for non-SPAM characteristics present. The total score is calculated and then action is taken based on its likelihood of being SPAM.
The filter does not assume that all arriving email is bad, rather that all email is neutral and should be considered equally.