Fortunately, HMCMC allows one to generate samples from the conditional probability distribution, given only the joint probability distribution (up to some constant). For more information on the HMCMC algorithm, we refer the reader to the numerous reviews on the topic. It is worth highlighting that our approach involves approximating the NMR spectrum as a probability distribution. This approximation introduces the potential for inaccuracies in the predicted chemical shifts, especially in spectral regions where significant overlap occurs. Nonetheless, the HMCMC algorithm accurately fits probability densities, leading to precise predictions of concentration in our case. Moreover, leveraging the representation of probability distribution of the NMR spectrum alongside the HMCMC technique accelerates convergence, compared to conventional methods like least squares minimization.