Propagation of uncertainties in unfolding procedures

A review of methods currently used to unfold particle spectra from measured pulse height distributions or other detector readings is given. It is pointed out that most of the measurements in particle spectrometry reveal ill-conditioned or ill-posed problems. The presentation which is given here for examples of such inverse problems is focussed on the algorithms used in the HEPRO unfolding program package of PTB. The question of uncertainty propagation is discussed for least-squares algorithms as well as for those based on maximum entropy. A first attempt has been made to quantify generally the “ambiguity” in ill-posed unfolding problems. The maximum entropy algorithm realized in the MIEKE code allows a clear distinction to be made between two parts of uncertainty, one part coming from ambiguity and one part coming from the usual uncertainty propagation. The resulting uncertainty matrix of the MIEKE code provides these two parts.