Bayesian analysis of 1D 1H-NMR spectra

Extracting spin system parameters from 1D high resolution ${}^1$H-NMR spectra can be an intricate task requiring sophisticate methods. With a few exceptions methods to perform such a total line shape analysis commonly rely on local optimization techniques which for increasing complexity of the underlying spin system tend to reveal local solutions. In this work we propose a full Bayesian modeling approach based on a quantum mechanical model of the spin system. The Bayesian formalism provides a global optimization strategy which allows to efficiently include prior knowledge about the spin system or to incorporate additional constraints concerning the parameters of interest. The proposed algorithm has been tested on synthetic and real 1D ${}^1$H-NMR data for various spin systems with increasing complexity. The results show that the Bayesian algorithm provides accurate estimates even for complex spectra with many overlapping regions, and that it can cope with symmetry induced local minima. By providing an unbiased estimate of the model evidence the proposed algorithm furthermore offers a way to discriminate between different spin system candidates.