In researching the needs for Abbon Laboratories in regards to their email server, I researched Naïve Bayesian Filters. Bayesian spam filtering; is a statistical technique of e-mail filtering. It makes use of a naive Bayes classifier to identify spam e-mail. The Bayesian classifiers work by associating the use of tokens (typically words, phrases, etc), with spam and non-spam e-mails and then using Bayesian inference to calculate a probability that an email is or is not spam. Bayesian spam filtering is considered to be a powerful procedure for dealing with spam, that can be tailored to the email needs of individual users, and gives low false positive spam detection rates that are generally acceptable to users.

The process of Bayesian spam filtering works in the way of distinguishing particular words which have a higher probability of occurring in spam email. This filter however, doesn’t know these probabilities in advance, and must be first trained so it can build them up. In order to train the filter, the user must first manually indicate whether a new email is spam or not. For all the words in each training email, the filter will adjust the probabilities that each word will appear in spam or legitimate email in its database. After training the system, the word probabilities are used to compute the probability that an email with a particular set of words in it belongs to a particular category. Each word in the email contributes to the email’s spam probability, or only the most interesting words. This contribution is called the posterior probability and is computed used Bayes’ theorem. The email’s spam probability is then computed over all words in the email and if the total exceeds a certain threshold, say 90%, the filter will then mark the email as spam. Then as with any other spam filtering technique email marked as spam can then be automatically sent to the “junk” or “spam” folder or can even be completely deleted. The software allows for adjustments during the training portion to make any modifications that are identified as false positives or false negatives. This allows the software to adapt to the evolving nature of spam.

Another advantage of the Bayesian spam filtering system is these email filters take advantage of Bayes' theorem. Bayes' theorem is used several times in the context of spam:
• a first time, to compute the probability that the message is spam, knowing that a given word appears in this message;
• a second time, to compute the probability that the message is spam, taking into consideration all of its words (or a relevant subset of them);
• sometimes a third time, to deal with rare words.

Some spam filters combine the results of both Bayesian spam filtering and other pre-defined rules about the contents, looking at the message's envelope, resulting in even higher filtering accuracy.

One of the main advantages of Bayesian spam filtering is that it can be trained on a per-user basis. The spam that a user receives is often related to the online user's activities. For example, a user may have been subscribed to an online newsletter that the user considers to be spam. This online newsletter is likely to contain words that are common to all newsletters, such as the name of the newsletter and its originating email address. A Bayesian spam filter will eventually assign a higher probability based on the user's specific patterns. The legitimate e-mails a user receives will have a tendency to be different. For example, in a corporate environment, the company name and the names of clients or customers will be mentioned often. The filter will assign a lower spam probability to emails containing those names. The word probabilities are unique to each user and can evolve over time with remedial training whenever the filter incorrectly classifies an email. As a result, Bayesian spam filtering accuracy after training is often greater to pre-defined rules.
Depending on the implementation, Bayesian spam filtering may be vulnerable to Bayesian poisoning, a technique used by spammers in an attempt to degrade the effectiveness of spam filters that rely on Bayesian filtering. A spammer practicing “Bayesian poisoning” will send out emails with large amounts of legitimate text which are gathered from legitimate news or literary sources. Spammer tactics include random safe words that are not normally associated with spam, thereby decreasing the email's spam score, making it more likely to slip past a Bayesian spam filter.