TY - GEN

T1 - Regression of Fluctuating System Properties

T2 - 37th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2017

AU - Verdoolaege, Geert

N1 - Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.

PY - 2018

Y1 - 2018

N2 - In various interesting physical systems, important properties or dynamics display a strongly fluctuating behavior that can best be described using probability distributions. Examples are fluid turbulence, plasma instabilities, textured images, porous media and cosmological structure. In order to quantitatively compare such phenomena, a similarity measure between distributions is needed, such as the Rao geodesic distance on the corresponding probabilistic manifold. This can form the basis for validation of theoretical models against experimental data and classification of regimes, but also for regression between fluctuating properties. This is the primary motivation for geodesic least squares (GLS) as a robust regression technique, with general applicability. In this contribution, we further clarify this motivation and we apply GLS to Tully–Fisher scaling of baryonic mass vs. rotation velocity in disk galaxies. We show that GLS is well suited to estimate the coefficients and tightness of the scaling. This is relevant for constraining galaxy formation models and for testing alternatives to the Lambda cold dark matter cosmological model.

AB - In various interesting physical systems, important properties or dynamics display a strongly fluctuating behavior that can best be described using probability distributions. Examples are fluid turbulence, plasma instabilities, textured images, porous media and cosmological structure. In order to quantitatively compare such phenomena, a similarity measure between distributions is needed, such as the Rao geodesic distance on the corresponding probabilistic manifold. This can form the basis for validation of theoretical models against experimental data and classification of regimes, but also for regression between fluctuating properties. This is the primary motivation for geodesic least squares (GLS) as a robust regression technique, with general applicability. In this contribution, we further clarify this motivation and we apply GLS to Tully–Fisher scaling of baryonic mass vs. rotation velocity in disk galaxies. We show that GLS is well suited to estimate the coefficients and tightness of the scaling. This is relevant for constraining galaxy formation models and for testing alternatives to the Lambda cold dark matter cosmological model.

KW - Information geometry

KW - Rao geodesic distance

KW - Regression analysis

KW - Tully-Fisher scaling

UR - http://www.scopus.com/inward/record.url?scp=85050276821&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-91143-4_8

DO - 10.1007/978-3-319-91143-4_8

M3 - Conference contribution

AN - SCOPUS:85050276821

SN - 9783319911427

T3 - Springer Proceedings in Mathematics and Statistics

SP - 77

EP - 87

BT - Bayesian Inference and Maximum Entropy Methods in Science and Engineering - MaxEnt 37, 2017

A2 - Louzada, Francisco

A2 - Stern, Julio

A2 - Takada, Hellinton

A2 - Polpo, Adriano

A2 - Izbicki, Rafael

PB - Springer New York LLC

Y2 - 9 July 2017 through 14 July 2017

ER -