Every source in the literature I could find about naive Bayes mentions using a gaussian's probability density function, using the mean and variance estimated from the data itself.
This strikes me as odd. If one estimates the variance and mean of the data (as opposed to has a prior assumption about it), than the distribution should be student t, not gaussian.
I recognize that the nuance may be unimportant in some cases, but still. This surprises me as it seems like using gaussian pdf is just a sort of mistake, and using the "correct" distribution has no cost involved. What am I missing here?