  We present a novel approach to the inference of spectral functions from
Euclidean time correlator data that makes close contact with modern Bayesian
concepts. Our method differs significantly from the maximum entropy method
(MEM). A new set of axioms is postulated for the prior probability, leading to
an improved expression, which is devoid of the asymptotically flat directions
present in the Shanon-Jaynes entropy. Hyperparameters are integrated out
explicitly, liberating us from the Gaussian approximations underlying the
evidence approach of the MEM. We present a realistic test of our method in the
context of the non-perturbative extraction of the heavy quark potential. Based
on hard-thermal-loop correlator mock data, we establish firm requirements in
the number of data points and their accuracy for a successful extraction of the
potential from lattice QCD. An improved potential estimation from previously
investigated quenched lattice QCD correlators is provided.
