Naïve Bayesian classifiers [1] are simple probabilistic classifiers with their foundation on application of Bayes’ theorem with the assumption of strong (naïve) independence among the features. The following equation [2] states Bayes’ theorem in mathematical terms:

$$P\left(A\right|B)=\frac{{\displaystyle P\left(A\right)P\left(B\right|A)}}{{\displaystyle P\left(B\right)}}$$

where:

*A* and *B* are events

*P*(*A*) and *P*(*B*) are the prior probabilities of *A* and *B* without regard to each other

*P*(*A*|*B*), also called *posterior probability*, is the probability of observing event *A* given that *B* is true

*P*(*B*|*A*), also called *likelihood*, is the probability of observing event *B* given that *A* is true

Suppose that vector **X** = (*x*_{1}, *x*_{2}, … *x _{n}*) is an instance (with

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