Macromolecular structures calculated from nuclear magnetic resonance data are not fully determined by experimental data but depend on subjective choices in data treatment and parameter settings. This makes it difficult to objectively judge the precision of the structures. We used Bayesian inference to derive a probability distribution that represents the unknown structure and its precision. This probability distribution also determines additional unknowns, such as theory parameters, that previously had to be chosen empirically. We implemented this approach by using Markov chain Monte Carlo techniques. Our method provides an objective figure of merit and improves structural quality.