On the Expectation-Maximization Unfolding with Smoothing

Abstract: Error propagation formulae are derived for the expectation-maximization iterative unfolding algorithm regularized by a smoothing step. The effective number of parameters in the fit to the observed data is defined for unfolding procedures. Based upon this definition, the Akaike information criterion is proposed as a principle for choosing the smoothing parameters in an automatic, data-dependent manner. The performance and the frequentist coverage of the resulting method are investigated using simulated samples. A number of issues of general relevance to all unfolding techniques are discussed, including irreducible bias, uncertainty increase due to a data-dependent choice of regularization strength, and presentation of results.