to fix the Pareto exchange rate at -2θ. The meansquared energy error depends on the type and number of observables used for refinement, and on the thermodynamic state. The article is organized as follows. In Sec. II A, we first introduce ensemble refinement with a focus on the Bayesian inference of ensembles (BioEn) method. We relate the KL divergence for Boltzmann distributions to the mean of the reduced energy difference in Sec. II B. We derive an approximation for the KL divergence as half the variance of the reduced energy difference in subsection II C. Moreover, the KL divergence is approximately symmetric with respect to its arguments. In subsection II D, we show that these approximations are exact in the Gaussian case. In subsection II F, we discuss how to use this information to encode our prior knowledge in the entropic prior used in BioEn and related methods. In subsection II G, we describe how to estimate the relevant energy uncertainty. We present three example systems in Sec. III. For these examples, we quantify the validity of the approximation of the KL divergence by the energy variance and illustrate the benefits and limits of gentle ensemble refinement in Sec. IV. In Sec. V, we discuss how we build prior knowledge about simulations. We end with Concluding Remarks in Sec. VI and the implication of our results for ill-defined inverse problems in general.