What if we could generate synthetic data for the Large Hadron Collider based entirely on first-principles theoretical calculations?  While this dream is hopelessly out of reach, we do have a growing catalog of precision calculations in quantum chromodynamics (QCD) as a well as increasingly accurate Monte Carlo generators.  In this talk, I show how to leverage ideas from information theory and machine learning to merge these disparate QCD predictions into a unified theoretical prediction with associated uncertainties.  Our strategy highlights the importance of logarithmic moments, which have not been previously studied in the QCD literature.