Database Reference
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mechanism to distinguish spam e-mail from legitimate e-mail. Many modern mail
clients implement variants of Bayesian spam filtering.
Naïve Bayes classifiers can also be used for fraud detection [11]. In the domain of
auto insurance, for example, based on a training set with attributes such as driver's
rating, vehicle age, vehicle price, historical claims by the policy holder, police
report status, and claim genuineness, naïve Bayes can provide probability-based
classification of whether a new claim is genuine [12].
7.2.1 Bayes' Theorem
The
conditional probability
of event C occurring, given that event A has
already occurred, is denoted as
, which can be found using the formula in
Equation 7.7
can be obtained with some minor algebra and substitution of the
conditional probability:
where C is the class label and A is the observed attributes
.
Equation 7.7
is the most common form of the
Bayes'
theorem
.
Mathematically, Bayes' theorem gives the relationship between the probabilities of
C
and
A
,
and
, and the conditional probabilities of
C
given
A
and
A
given
C
, namely
and
.
Bayes' theorem is significant because quite often is much more difficult to
compute than and from the training data. By using Bayes' theorem,
this problem can be circumvented.
An example better illustrates the use of Bayes' theorem. John flies frequently and
likes to upgrade his seat to first class. He has determined that if he checks in for
his flight at least two hours early, the probability that he will get an upgrade is
0.75; otherwise, the probability that he will get an upgrade is 0.35. With his busy
