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Robust approaches for inverse problems based on Tsallis and Kaniadakis generalised statistics
The inference of physical parameters from measured data is essential for describing and analysing several complex systems. In this regard, the inverse problem theory has been applied to solve this task based on the Boltzmann–Gibbs statistical mechanics by considering that the errors are Gaussian-lik...
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Published in: | European physical journal plus 2021-05, Vol.136 (5), p.518, Article 518 |
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Main Authors: | , , , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | The inference of physical parameters from measured data is essential for describing and analysing several complex systems. In this regard, the inverse problem theory has been applied to solve this task based on the Boltzmann–Gibbs statistical mechanics by considering that the errors are Gaussian-like. However, in the non-Gaussian noise case, the classical inverse-problem approach estimates model parameters which may be inaccurate and grossly biased. In the case of extreme outliers in the data set, for example, the most common approach used is based on the
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-norm of the difference between modelled and observed data. This approach is famous for being robust because it is based on a long-tailed probability function: the Laplace distribution. However,
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-norm-based inverse problems equally weight noise and information, which limits its robustness to a large number of outliers in the data set. To mitigate the limitations of the
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-norm approach, we introduce in this work the inverse problem theory in the context of Tsallis and Kaniadakis generalised statistical mechanics, by generalising the Laplace distribution. Applications to a classical geophysical data-inversion problem demonstrate that inverse problems based on Tsallis
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- and Kaniadakis
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-statistics outperform the classical and
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-norm-based frameworks. They also reveal that the best results are associated with the limit in which both generalised distributions are equivalent. |
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ISSN: | 2190-5444 2190-5444 |
DOI: | 10.1140/epjp/s13360-021-01521-w |