Here, ⟨y i ⟩ = N α=1 w α y α i are the averages of the calculated observables y α i for conformation α with indices i = 1, . . . , M for the measured averages Y i with associated errors σ i , both theoretical and experimental. The theoretical errors primarily reflect uncertainties in calculating the observables y(x) for given conformations x using simplified models of the experiment. By contrast, we account for errors in the weights in the entropic prior, Eq. ( ), through the confidence parameter θ. Note that the structural ensembles do not have to come from molecular simulations and that the data do not necessarily have to be from experiment.