This question already has an answer here:
Say you have $n$ different, non-normal, potentially overlapping data sets of samples. Maybe their densities look something like:
and you are given a new sample $x$, how would you decide to which of these sample sets it would most likely belong?
I would assume it is possible to do a (kernel) density estimation of each of the sample sets, interpolate them to functions $p_n$, and then calculate $p_n(x)$ for each, selecting the one with the highest probability.
However both the decision rule and the method seem, well, off. Can anybody help me in getting a better intuition of this problem?
EDIT Say the data comes from a continuous scoring system, like a depression scale, and I have annotated data for many different subjects. So I can get the density plots for "severe", "mildly" and "non-depressed" subjects. Now I have a new sample and wish to know (based on the score) which the person most likely belongs to.