{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:24:23Z","timestamp":1760243063965,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2015,7,1]],"date-time":"2015-07-01T00:00:00Z","timestamp":1435708800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In regression analysis 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. In many situations, the assumptions underlying OLS are not fulfilled, and several other approaches have been proposed. However, most techniques address only part of the shortcomings of OLS. We here discuss a new and more general regression method, which we call geodesic least squares regression (GLS). The method is based on minimization of the Rao geodesic distance on a probabilistic manifold. For the case of a power law, we demonstrate the robustness of the method on synthetic data in the presence of significant uncertainty on both the data and the regression model. We then show good performance of the method in an application to a scaling law in magnetic confinement fusion.<\/jats:p>","DOI":"10.3390\/e17074602","type":"journal-article","created":{"date-parts":[[2015,7,1]],"date-time":"2015-07-01T10:00:34Z","timestamp":1435744834000},"page":"4602-4626","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A New Robust Regression Method Based on Minimization of Geodesic Distances on a Probabilistic Manifold: Application to Power Laws"],"prefix":"10.3390","volume":"17","author":[{"given":"Geert","family":"Verdoolaege","sequence":"first","affiliation":[{"name":"Department of Applied Physics, Ghent University, Sint-Pietersnieuwstraat 41, B-9000 Ghent, Belgium"},{"name":"Laboratory for Plasma Physics\u2014Royal Military Academy (LPP-ERM\/KMS), Avenue de la Renaissancelaan 30, B-1000 Brussels, Belgium\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,7,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"S18","DOI":"10.1088\/0029-5515\/47\/6\/S02","article-title":"Chapter 2: Plasma confinement and transport","volume":"47","author":"Doyle","year":"2007","journal-title":"Nucl. Fusion."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1887","DOI":"10.1890\/11-0538.1","article-title":"On the use of log-transformations vs. nonlinear regression for analyzing biological power laws","volume":"92","author":"Xiao","year":"2011","journal-title":"Ecology"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"A439","DOI":"10.1088\/0741-3335\/48\/5A\/S45","article-title":"The impact of statistical models on scalings derived from multi-machine H-mode threshold experiments","volume":"48","author":"McDonald","year":"2006","journal-title":"Plasma Phys. Control. Fusion."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1063\/1.4903708","article-title":"Geodesic least squares regression on information manifolds","volume":"1636","author":"Verdoolaege","year":"2013","journal-title":"AIP Conf. Proc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1063\/1.4906023","article-title":"Geodesic least squares regression for scaling studies in magnetic confinement fusion","volume":"1641","author":"Verdoolaege","year":"2014","journal-title":"AIP Conf. Proc."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Basu, A., Shioya, H., and Park, C. (2011). Statistical Inference: The Minimum Distance Approach, Chapman & Hall\/CRC.","DOI":"10.1201\/b10956"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"McCullagh, P., and Nelder, J. (1989). Generalized Linear Models, Chapman & Hall\/CRC. [2nd].","DOI":"10.1007\/978-1-4899-3242-6"},{"key":"ref_8","unstructured":"Amari, S., and Nagaoka, H. (2000). 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Imaging Vis."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/7\/4602\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:48:38Z","timestamp":1760215718000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/7\/4602"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,1]]},"references-count":37,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2015,7]]}},"alternative-id":["e17074602"],"URL":"https:\/\/doi.org\/10.3390\/e17074602","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2015,7,1]]}}}