This question sounds ridiculous, let me clarify motivation:
Fisher information & Bayesian inference uncertainty seemed very cool to me because they can effectively tell you "how representative your sample is". But they do this via uncertainty in distribution/model parameters.
I was wondering if it is possible to do something similar for free form (or non-parametric) distributions (e.g. uncertainty in KDE). Or whether the assumptions made about a distribution in parametric statistics is somehow required to answer the question of "how representative is my sample"?
P.S. Unlike this poster I'm not trying to encode known uncertainties but to detect uncertainties in non-parameteric distributions (e.g. KDE).