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Title: Geodesic least squares regression for scaling studies in magnetic confinement fusion

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.
Authors:
 [1]
  1. Department of Applied Physics, Ghent University, Ghent, Belgium and Laboratory for Plasma Physics, Royal Military Academy, Brussels (Belgium)
Publication Date:
OSTI Identifier:
22390873
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1641; Journal Issue: 1; Conference: MAXENT 2014: Conference on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Clos Luce, Amboise (France), 21-26 Sep 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; GEODESICS; LEAST SQUARE FIT; MAGNETIC CONFINEMENT; MATHEMATICAL MANIFOLDS; MATHEMATICAL MODELS; PROBABILISTIC ESTIMATION; REGRESSION ANALYSIS; SCALING LAWS