An algorithm for automatic unfolding of one-dimensional data distributions

We discuss a non-parametric algorithm to unfold detector effects from one-dimensional data distributions. Unfolding is performed by fitting a flexible spline model to the data using an unbinned maximum-likelihood method while employing a smooth regularisation that maximises the relative entropy of the solution with respect to an a priori guess. A regularisation weight is picked automatically such that it minimises the mean integrated squared error of the fit. The algorithm scales to large data sets by employing an adaptive binning scheme in regions of high density. An estimate of the uncertainty of the solution is provided and shown to be accurate by studying the frequentist properties of the algorithm in Monte-Carlo simulations. The simulations show that the regularisation bias decreases as the sample size increases.