# Independent variables in Naïve Bayes

In the perfect explanation of Bayes' Theorem here as far as I know features of the class should be independent. The question is how to prove statistically that two given features are independent? I know Chi-test and Principal Component Analysis so far for analysing independence of two given variables. Is it sufficient to analyse with Chi-test independence of variables?

Note that the easy way to say that two variables are independent is to see their correlation, but sometimes it is not sufficient to say that two variables are not independent when there is no correlation between them.

Hope I could explain my question.