  The extraction of spectral densities from Euclidean correlators evaluated on
the lattice is an important problem, as these quantities encode physical
information on scattering amplitudes, finite-volume spectra, inclusive decay
rates, and transport coefficients. In this contribution, we show that the
Bayesian approach to this "inverse" problem, based on Gaussian processes, can
be reformulated in a way that yields a solution equivalent, up to statistical
uncertainties, to the one obtained in a Backus-Gilbert approach. After
discussing this equivalence, we point out its implications for a reliable
determination of spectral densities from lattice simulations.
