@inproceedings{4318202,
  abstract     = {{The study of the scaling of key physical parameters characterizing a system, in terms of a number of other parameters that can be measured or controlled, is a practice that is useful in many areas of science such as astrophysics, biology and in general in complex physical systems. In fusion science, the scaling of various quantities is often conveniently expressed as a power law. Notable examples include the scaling of the thermal energy confinement time $\tau_\mathrm{th}$ and the power threshold $P_\mathrm{thr}$ for the L-to-H transition, which we take in this work as case studies for benchmarking our methods. From the methodological point of view, most efforts targeted at deriving scaling laws in fusion have been concentrated on the power law form, leading to a linear regression problem on a logarithmic scale. However, concerns have been raised about the validity of a Gaussian error model on the logarithmic scale, while the assumption of a negligible error bar on the independent variables has been challenged as well. In this contribution we present a novel regression method targeted at situations with significant uncertainty on both the dependent and independent variables or with non-Gaussian distribution models. Unlike the classic regression model, the conditional distribution of the dependent variable suggested by the data (`observed distribution'), need not be the same as the modeled distribution. Indeed, the purpose of our regression analysis is to fit a regression model to the complete conditional distribution of the dependent variable, not only its mean. In the mathematical field of information geometry, probability distributions are represented in a Riemannian space---or information manifold---with the Fisher information acting as a metric tensor. One can use this framework to calculate the geodesic distance as a natural and mathematically well-founded similarity measure between probability distributions. This allows us to perform a regression analysis of the observed conditional distributions of the dependent variable as a function of the modeled distribution, written in terms of the distributions of the independent variables. To do this, we compare the observed distributions with the modeled distribution by means of the geodesic distance. The advantage of our technique is, on the one hand, that the uncertainty, and indeed the complete statistics, of each variable is taken into account in order to derive the regression law itself. On the other hand, arbitrary sophisticated probability models may be used for describing the data, for instance by including the measurement forward model, which potentially leads to more reliable scaling expressions. We demonstrate our method by deriving scaling laws for $\tau_\mathrm{th}$ and $P_\mathrm{thr}$ from data in the international databases. We show that, even in the simplest case assuming Gaussian statistics with the standard deviation determined by the error bar, our method leads to a considerably improved goodness-of-fit compared to the results obtained by ordinary linear regression and errors-in-variables techniques. Future work will concern the application of our method for deriving other scaling laws in cases where considerable error bars or non-Gaussian statistics may play an important role.}},
  author       = {{Verdoolaege, Geert and Shabbir, Aqsa and Noterdaeme, Jean-Marie}},
  booktitle    = {{11th Meeting of the ITPA Transport and Confinement Topical Group, Abstracts}},
  keywords     = {{nuclear fusion,magnetic confinement,geodesic distance,Regression,information geometry,scaling laws}},
  language     = {{eng}},
  location     = {{Fukuoka, Japan}},
  title        = {{A new technique for estimating fusion scaling laws via regression on an information manifold}},
  year         = {{2013}},
}