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

Authors

Steffen Schön, Leibniz University HannoverFollow
Gaël Kermarrec, Leibniz University HannoverFollow
Boris Kargoll, Leibniz University HannoverFollow
Ingo Neumann, Leibniz University HannoverFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

6-2017

Comments

Technical Report: UTEP-CS-17-65

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.