# 3

# Naïve Bayes Classifier

A naïve Bayes classifier is based on the Bayes theorem. Hence, this chapter first reviews the Bayes theorem and then describes naïve Bayes classifier. A list of data mining software packages that support the learning of a naïve Bayes classifier is provided. Some applications of naïve Bayes classifiers are given with references.

## 3.1 Bayes Theorem

Given two events *A* and *B*, the conjunction (∧) of the two events represents the occurrence of both *A* and *B*. The probability, *P*(*A* ∧ *B*) is computed using the probability of *A* and *B*, *P*(*A*) and *P*(*B*), and the conditional probability of *A* given *B*, *P*(*A*|*B*), or *B* given *A*, *P*(*B*|*A*):

$P\left(A\wedge B\right)=P\left(A|B\right)P\left(B\right)=P\left(B|A\right)P\left(A\right).$ |
(3.1) |

The Bayes theorem is derived from Equation 3.1:

$P(A|$ |

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