How should one formulate, extract and interpret 'non-observables' for nuclei?

Nuclear observables such as binding energies and cross sections can be directly measured. Other physically useful quantities, such as spectroscopic factors, are related to measured quantities by a convolution whose decomposition is not unique. Can a framework for these nuclear structure 'non-observables' be formulated systematically so that they can be extracted from experiment with known uncertainties and calculated with consistent theory? Parton distribution functions in hadrons serve as an illustrative example of how this can be done. A systematic framework is also needed to address questions of interpretation, such as whether short-range correlations are important for nuclear structure.