Methods and related systems are described for extracting information about a system of nuclear spins including: performing a plurality of Nuclear Magnetic Resonance (NMR) measurements on the system of nuclear spins; acquiring NMR data from each of the plurality of NMR measurements; performing data inversion using an random-sampler to generate an ensemble of spectra so as to extract information about the system of nuclear spins; and analyzing the performed random-sampler inversion results to extract information about the system of nuclear spins.