An approach utilizing Bayesian probability acid NMR chemical shifts to derive structural information about proteins is presented. The method is based on measurement of a spectroscopic parameter, P (such as a chemical shift or a coupling constant), which is then transformed via use of a corresponding parameter surface, P(alpha,beta), into an unnormalized torsion angle probability or Z surface, Z(alpha,beta). Using empirically determined parameter surfaces, the backbone phi,psi error between prediction and experiment is about 17 degrees, but for 10 Ala residues in Staphylococcal nuclease, this reduces to similar to 10 degrees when quantum mechanically computed C-13 Shielding surfaces are utilized. The Z-surface approach permits unique combination of a wide variety of spectroscopic observables for refinement and prediction of protein structure in both solution- or solid-state systems.