Relating probability distributions using geodesic least squares regression: Application to edge-localized modes in fusion plasmas

Geodesic least squares regression (GLS) is a new robust, but simple regression technique based on minimization of the Rao geodesic distance on a probabilistic manifold. It is particularly useful in the presence of large or unknown sources of uncertainty, as it relates probability distributions rather than individual measurements. The GLS method is employed here to estimate the dependence between the probability distributions of two important characteristics of a repetitive instability occurring in the boundary region of fusion plasmas, namely the edge-localized mode (ELM). Specifically, we study the relation between the plasma energy loss following an ELM and the time since the previous ELM. GLS is shown to produce consistent results, whether using measurements on individual ELMs or averaged quantities, even in the presence of questionable modeling assumptions. The method is illustrated using the pseudosphere as an intuitive model of the Gaussian manifold.