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 -