  Bayesian classifiers perform well when each of the features is completely
independent of the other which is not always valid in real world application.
The aim of this study is to implement and compare the performances of each
variant of Bayesian classifier (Multinomial, Bernoulli, and Gaussian) on
anomaly detection in network intrusion, and to investigate whether there is any
association between each variant assumption and their performance. Our
investigation showed that each variant of Bayesian algorithm blindly follows
its assumption regardless of feature property, and that the assumption is the
single most important factor that influences their accuracy. Experimental
results show that Bernoulli has accuracy of 69.9% test (71% train), Multinomial
has accuracy of 31.2% test (31.2% train), while Gaussian has accuracy of 81.69%
test (82.84% train). Going deeper, we investigated and found that each Naive
Bayes variants performances and accuracy is largely due to each classifier
assumption, Gaussian classifier performed best on anomaly detection due to its
assumption that features follow normal distributions which are continuous,
while multinomial classifier have a dismal performance as it simply assumes
discreet and multinomial distribution.
