For the optimal weights obtained by BioEn, the energy uncertainties calculated in the space of conformations x and of observables y are equal, ⟨∆u⟩ p = ⟨∆v⟩ p(y) (see Appendix C) and var p (∆u) ≈ var p(y) (∆v) in gentle ensemble refinement. The underlying reason is that in the BioEn optimal solution, the factor scaling the relative weight of conformation x depends only on y(x), not on x directly. Conformations with the same value of y are thus treated equally.