Generalized statistics: Applications to data inverse problems with outlier-resistance.

Autor: Dos Santos Lima GZ; School of Science and Technology, Federal University of Rio Grande do Norte, Natal, RN, Brazil., de Lima JVT; Department of Theoretical and Experimental Physics, Federal University of Rio Grande do Norte, Natal, RN, Brazil., de Araújo JM; Department of Theoretical and Experimental Physics, Federal University of Rio Grande do Norte, Natal, RN, Brazil., Corso G; Department of Biophysics and Pharmacology, Federal University of Rio Grande do Norte, Natal, RN, Brazil., da Silva SLEF; Department of Applied Science and Technology, Politecnico di Torino, Turin, TO, Italy.; GISIS, Fluminense Federal University, Niterói, RJ, Brazil.
Jazyk: angličtina
Zdroj: PloS one [PLoS One] 2023 Mar 30; Vol. 18 (3), pp. e0282578. Date of Electronic Publication: 2023 Mar 30 (Print Publication: 2023).
DOI: 10.1371/journal.pone.0282578
Abstrakt: The conventional approach to data-driven inversion framework is based on Gaussian statistics that presents serious difficulties, especially in the presence of outliers in the measurements. In this work, we present maximum likelihood estimators associated with generalized Gaussian distributions in the context of Rényi, Tsallis and Kaniadakis statistics. In this regard, we analytically analyze the outlier-resistance of each proposal through the so-called influence function. In this way, we formulate inverse problems by constructing objective functions linked to the maximum likelihood estimators. To demonstrate the robustness of the generalized methodologies, we consider an important geophysical inverse problem with high noisy data with spikes. The results reveal that the best data inversion performance occurs when the entropic index from each generalized statistic is associated with objective functions proportional to the inverse of the error amplitude. We argue that in such a limit the three approaches are resistant to outliers and are also equivalent, which suggests a lower computational cost for the inversion process due to the reduction of numerical simulations to be performed and the fast convergence of the optimization process.
Competing Interests: The authors have declared that no competing interests exist.
(Copyright: © 2023 dos Santos Lima et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)
Databáze: MEDLINE
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