Analysis of distorted measurements -- parameter estimation and unfolding

Parameter inference from distorted measurements is discussed. 2. Smeared measurements are unfolded without explicit regularization. The corresponding results are unbiased and permit to fit parameters and to apply quantitative goodness-of-fit tests. 3. Common unfolding methods (iterative EM with early stopping, truncated SVD, ML fits with curvature, entropy and norm penalties) are tested and compared to each other with the regularization parameter adjusted to minimize the integrated square error (ISE) in all cases. Apart from histogram representations, spline approximations are considered. All simulations indicate that the EM method leads to smaller ISEs than the competing approaches. Especially promising is the EM unfolding to spline approximations. The studies are based on different distributions, event numbers, resolutions and enough independent simulations to obtain conclusive results. It is proposed to unfold data with the EM method to b-spline approximations and to supplement the results with histograms and error matrices obtained by unfolding into relative wide bins without explicit regularization.

Parameter inference from distorted measurements is discussed. 2. Smeared measurements are unfolded without explicit regularization. The corresponding results are unbiased and permit to fit parameters and to apply quantitative goodness-of-fit tests. 3. Common unfolding methods (iterative EM with early stopping, truncated SVD, ML fits with curvature, entropy and norm penalties) are tested and compared to each other with the regularization parameter adjusted to minimize the integrated square error (ISE) in all cases. Apart from histogram representations, spline approximations are considered. All simulations indicate that the EM method leads to smaller ISEs than the competing approaches. Especially promising is the EM unfolding to spline approximations. The studies are based on different distributions, event numbers, resolutions and enough independent simulations to obtain conclusive results. It is proposed to unfold data with the EM method to b-spline approximations and to supplement the results with histograms and error matrices obtained by unfolding into relative wide bins without explicit regularization.

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