  We implement the Bayesian inference to retrieve energy spectra of all
neutrinos from a galactic core-collapse supernova (CCSN). To achieve high
statistics and full sensitivity to all flavours of neutrinos, we adopt a
combination of several reaction channels from different large-scale neutrino
observatories, namely inverse beta decay on proton and elastic scattering on
electron from Hyper-Kamiokande (Hyper-K), charged current absorption on Argon
from Deep Underground Neutrino Experiment (DUNE) and coherent elastic
scattering on Lead from RES-NOVA. Assuming no neutrino oscillation or specific
oscillation models, we obtain mock data for each channel through Poisson
processes with the predictions, for a typical source distance of 10 kpc in our
Galaxy, and then evaluate the probability distributions for all spectral
parameters of theoretical neutrino spectrum model with Bayes' theorem. Although
the results for either the electron-neutrinos or electron-antineutrinos reserve
relatively large uncertainties (according to the neutrino mass hierarchy), a
precision of a few percent (i.e., $\pm 1 \% \sim \pm 4 \%$ at a credible
interval of $2 \sigma$) is achieved for primary spectral parameters (e.g., mean
energy and total emitted energy) of other neutrino species. Moreover, the
correlation coefficients between different parameters are computed as well and
interesting patterns are found. Especially, the mixing-induced correlations are
sensitive to the neutrino mass hierarchy, which potentially makes it a brand
new probe to determine the neutrino mass hierarchy in the detection of galactic
supernova neutrinos. Finally, we discuss the origin of such correlation
patterns and perspectives for further improvement on our results.
