TY - GEN
T1 - Geodesic least squares regression for scaling studies in magnetic confinement fusion
AU - Verdoolaege, Geert
N1 - Publisher Copyright:
© 2015 AIP Publishing LLC.
PY - 2015
Y1 - 2015
N2 - In regression analyses for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to scaling laws. We here discuss a new regression method that is robust in the presence of significant uncertainty on both the data and the regression model. The method, which we call geodesic least squares regression (GLS), is based on minimization of the Rao geodesic distance on a probabilistic manifold. We demonstrate the superiority of the method using synthetic data and we present an application to the scaling law for the power threshold for the transition to the high confinement regime in magnetic confinement fusion devices.
AB - In regression analyses for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to scaling laws. We here discuss a new regression method that is robust in the presence of significant uncertainty on both the data and the regression model. The method, which we call geodesic least squares regression (GLS), is based on minimization of the Rao geodesic distance on a probabilistic manifold. We demonstrate the superiority of the method using synthetic data and we present an application to the scaling law for the power threshold for the transition to the high confinement regime in magnetic confinement fusion devices.
KW - information geometry
KW - nuclear fusion
KW - regression
KW - scaling laws
UR - https://www.scopus.com/pages/publications/84940539667
U2 - 10.1063/1.4906023
DO - 10.1063/1.4906023
M3 - Conference contribution
AN - SCOPUS:84940539667
T3 - AIP Conference Proceedings
SP - 564
EP - 571
BT - Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014
A2 - Mohammad-Djafari, Ali
A2 - Barbaresco, Frederic
A2 - Barbaresco, Frederic
PB - American Institute of Physics Inc.
T2 - 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014
Y2 - 21 September 2014 through 26 September 2014
ER -