Regularization and error assignment to unfolded distributions

The commonly used approach to present unfolded data only in graphical formwith the diagonal error depending on the regularization strength is unsatisfac-tory. It does not permit the adjustment of parameters of theories, the exclusionof theories that are admitted by the observed data and does not allow the com-bination of data from different experiments. We propose fixing the regulariza-tion strength by a p-value criterion, indicating the experimental uncertaintiesindependent of the regularization and publishing the unfolded data in additionwithout regularization. These considerations are illustrated with three differentunfolding and smoothing approaches applied to a toy example.