  The detection of neutrinos from SN 1987A by the Kamiokande-II and
Irvine-Michigan-Brookhaven detectors provided the first glimpse of core
collapse in a supernova, complementing the optical observations and confirming
our basic understanding of the mechanism behind the explosion. One
long-standing puzzle is that, when fitted with thermal spectra, the two
independent detections do not seem to agree with either each other or typical
theoretical expectations. We assess the compatibility of the two data sets in a
model-independent way and show that they can be reconciled if one avoids any
bias on the neutrino spectrum stemming from theoretical conjecture. We
reconstruct the neutrino spectrum from SN 1987A directly from the data through
non-parametric inferential statistical methods and present predictions for the
Diffuse Supernova Neutrino Background based on SN 1987A data. We show that this
prediction cannot be too small (especially in the 10-18 MeV range), since the
majority of the detected events from SN 1987 were above 18 MeV (including 6
events above 35 MeV), suggesting an imminent detection in operational and
planned detectors.
