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An outlier-resistant κ-generalized approach for robust physical parameter estimation

Author

Listed:
  • da Silva, Sérgio Luiz E.F.
  • Silva, R.
  • dos Santos Lima, Gustavo Z.
  • de Araújo, João M.
  • Corso, Gilberto

Abstract

In this work we propose a robust methodology to mitigate the undesirable effects caused by outliers to generate reliable physical models. In this way, we formulate the inverse problems theory in the context of Kaniadakis statistical mechanics (or κ-statistics), in which the classical approach is a particular case. In this regard, the errors are assumed to be distributed according to a finite-variance κ-generalized Gaussian distribution. Based on the probabilistic maximum-likelihood method we derive a κ-objective function associated with the finite-variance κ-Gaussian distribution. To demonstrate our proposal’s outlier-resistance, we analyze the robustness properties of the κ-objective function with help of the so-called influence function. In this regard, we discuss the role of the entropic index (κ) associated with the Kaniadakis κ-entropy in the effectiveness in inferring physical parameters by using strongly noisy data. In this way, we consider a classical geophysical data-inverse problem in two realistic circumstances, in which the first one refers to study the sensibility of our proposal to uncertainties in the input parameters, and the second is devoted to the inversion of a seismic data set contaminated by outliers. The results reveal an optimum κ-value at the limit κ→2/3, which is related to the best results.

Suggested Citation

  • da Silva, Sérgio Luiz E.F. & Silva, R. & dos Santos Lima, Gustavo Z. & de Araújo, João M. & Corso, Gilberto, 2022. "An outlier-resistant κ-generalized approach for robust physical parameter estimation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    • Handle: RePEc:eee:phsmap:v:600:y:2022:i:c:s0378437122003855
    DOI: 10.1016/j.physa.2022.127554
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    References listed on IDEAS

    as
    1. Sérgio Luiz E F da Silva & Pedro T C Carvalho & Carlos A N da Costa & João M de Araújo & Gilberto Corso, 2020. "An objective function for full-waveform inversion based on frequency-dependent offset-preconditioning," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-15, October.
    2. Amelia Carolina Sparavigna, 2015. "Tsallis and Kaniadakis Entropic Measures in Polytropic, Logarithmic and Exponential Functions," International Journal of Sciences, Office ijSciences, vol. 4(11), pages 1-4, November.
    3. Hasegawa, Yoshihiko & Arita, Masanori, 2009. "Properties of the maximum q-likelihood estimator for independent random variables," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3399-3412.
    4. da Silva, Sérgio Luiz Eduardo Ferreira & dos Santos Lima, Gustavo Zampier & de Araújo, João Medeiros & Corso, Gilberto, 2021. "Extensive and nonextensive statistics in seismic inversion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    5. da Silva, Sérgio Luiz Eduardo Ferreira & da Costa, Carlos A.N. & Carvalho, Pedro Tiago C. & de Araújo, João Medeiros & dos Santos Lucena, Liacir & Corso, Gilberto, 2020. "Robust full-waveform inversion using q-statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    6. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    7. Soares, Bráulio B. & Barboza, Edésio M. & Abreu, Everton M.C. & Neto, Jorge Ananias, 2019. "Non-Gaussian thermostatistical considerations upon the Saha equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 532(C).
    8. G. Kaniadakis, 2009. "Maximum entropy principle and power-law tailed distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 70(1), pages 3-13, July.
    9. Sérgio Luiz E. F. Silva & Gilberto Corso, 2021. "Nonextensive Gutenberg–Richter law and the connection between earthquakes and marsquakes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(1), pages 1-5, January.
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