# What non-Bayesian classifiers could be used in a naive Bayes model?

Bayes' theorem [is used] in the classifier's decision rule, but naive Bayes is not (necessarily) a Bayesian method.

I have applied naive Bayes assumption to LDA, but it has a Bayes classifier as the sole classifier. To what other non-Bayesian classifiers or learning models could the naive Bayes assumption be applied?

• This question seems clear enough to me. I'm voting to leave open. – gung - Reinstate Monica Feb 8 '17 at 16:46

Before commencing, however, some clarification of the word 'Bayes' in this context is appropriate. In work on supervised classification methods it has become standard to refer to the $P(i)$ as the class $i$ prior probability, because this gives the probability that an object will belong to class $i$ prior to observing any information about the object. Combining the prior with $P(\mathbf x \mid i)$, as shown above, gives the posterior probability, after having observed $\mathbf x$. This combination is effected via Bayes theorem, and it is because of this that 'Bayes' is used in the name of these methods. [...] The important point for us is that no notion of subjective probability is introduced: the methods are not [necessarily] 'Bayesian' in the formal statistical sense. [...] In this paper, following almost all the work on the idiot's Bayes method, we adopt a frequentist interpretation.