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Why Student Distributions? Why Matern’s Covariance Model? A Symmetry-Based Explanation

  • Stephen Schön
  • Gael Kermarrec
  • Boris Kargoll
  • Ingo Neumann
  • Olga Kosheleva
  • Vladik KreinovichEmail author
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 760)

Abstract

In this paper, we show that empirical successes of Student distribution and of Matern’s covariance models can be indirectly explained by a natural requirement of scale invariance – that fundamental laws should not depend on the choice of physical units. Namely, while neither the Student distributions nor Matern’s covariance models are themselves scale-invariant, they are the only one which can be obtained by applying a scale-invariant combination function to scale-invariant functions.

Notes

Acknowledgments

This work was performed when Olga Kosheleva and Vladik Kreinovich were visiting researchers with the Geodetic Institute of the Leibniz University of Hannover, a visit supported by the German Science Foundation. This work was also supported in part by NSF grant HRD-1242122.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Stephen Schön
    • 1
  • Gael Kermarrec
    • 1
  • Boris Kargoll
    • 1
  • Ingo Neumann
    • 1
  • Olga Kosheleva
    • 2
  • Vladik Kreinovich
    • 2
    Email author
  1. 1.Leibniz Universität HannoverHannoverGermany
  2. 2.University of Texas at El PasoEl PasoUSA

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