  The statistical models used to derive the results of experimental analyses
are of incredible scientific value and are essential information for analysis
preservation and reuse. In this paper, we make the scientific case for
systematically publishing the full statistical models and discuss the technical
developments that make this practical. By means of a variety of physics cases
-- including parton distribution functions, Higgs boson measurements, effective
field theory interpretations, direct searches for new physics, heavy flavor
physics, direct dark matter detection, world averages, and beyond the Standard
Model global fits -- we illustrate how detailed information on the statistical
modelling can enhance the short- and long-term impact of experimental results.
