Convergence and error propagation results on a linear iterative unfolding method
| Title: | Convergence and error propagation results on a linear iterative unfolding method |
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| Authors: | Laszlo, Andras |
| Source: | SIAM/ASA Journal of Uncertainty Quantification 4 (2016) 1345 |
| Publication Year: | 2014 |
| Collection: | Mathematics Physics (Other) Statistics |
| Subject Terms: | Statistics - Applications, Mathematics - Statistics Theory, Physics - Data Analysis, Statistics and Probability, 62H99 (Primary) 46E30, 46E27 (Secondary) |
| More Details: | Unfolding problems often arise in the context of statistical data analysis. Such problematics occur when the probability distribution of a physical quantity is to be measured, but it is randomized (smeared) by some well understood process, such as a non-ideal detector response or a well described physical phenomenon. In such case it is said that the original probability distribution of interest is folded by a known response function. The reconstruction of the original probability distribution from the measured one is called unfolding. That technically involves evaluation of the non-bounded inverse of an integral operator over the space of L^1 functions, which is known to be an ill-posed problem. For the pertinent regularized operator inversion, we propose a linear iterative formula and provide proof of convergence in a probability theory context. Furthermore, we provide formulae for error estimates at finite iteration stopping order which are of utmost importance in practical applications: the approximation error, the propagated statistical error, and the propagated systematic error can be quantified. The arguments are based on the Riesz-Thorin theorem mapping the original L^1 problem to L^2 space, and subsequent application of ordinary L^2 spectral theory of operators. A library implementation in C of the algorithm along with corresponding error propagation is also provided. A numerical example also illustrates the method in operation. Comment: 27 pages, 1 figure |
| Document Type: | Working Paper |
| DOI: | 10.1137/15M1035744 |
| Access URL: | http://arxiv.org/abs/1404.2787 |
| Accession Number: | edsarx.1404.2787 |
| Database: | arXiv |
| DOI: | 10.1137/15M1035744 |
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