Densities mixture unfolding for data obtained from detectors with finite resolution and limited acceptance
Abstract
A procedure based on a Mixture Density Model for correcting experimental data for distortions due to finite resolution and limited detector acceptance is presented. Addressing the case that the solution is known to be nonnegative, in the approach presented here, the true distribution is estimated by a weighted sum of probability density functions with positive weights and with the width of the densities acting as a regularization parameter responsible for the smoothness of the result. To obtain better smoothing in less populated regions, the width parameter is chosen inversely proportional to the square root of the estimated density. Furthermore, the nonnegative garrote method is used to find the most economic representation of the solution. Crossvalidation is employed to determine the optimal values of the resolution and garrote parameters. The proposed approach is directly applicable to multidimensional problems. Numerical examples in one and two dimensions are presented to illustrate the procedure.
 Publication:

Nuclear Instruments and Methods in Physics Research A
 Pub Date:
 April 2015
 DOI:
 10.1016/j.nima.2015.01.014
 arXiv:
 arXiv:1410.1586
 Bibcode:
 2015NIMPA.778...92G
 Keywords:

 Deconvolution;
 Mixture densities;
 Adaptive algorithm;
 Inverse problem;
 Single sided strongly varying spectra;
 Regularization;
 Physics  Data Analysis;
 Statistics and Probability;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 High Energy Physics  Experiment;
 Nuclear Experiment;
 Statistics  Applications;
 6207 (Primary);
 62F03;
 62F10;
 62P35;
 62P30 (Secondary)
 EPrint:
 26 pages, 15 figures