title: Model selection for identifying power-law scaling.
abstract: Long-range temporal and spatial correlations have been reported in a remarkable number of studies. In particular power-law scaling in neural activity raised considerable interest. We here provide a straightforward algorithm not only to quantify power-law scaling but to test it against alternatives using (Bayesian) model comparison. Our algorithm builds on the well-established detrended fluctuation analysis (DFA). After removing trends of a signal, we determine its mean squared fluctuations in consecutive intervals. In contrast to DFA we use the values per interval to approximate the distribution of these mean squared fluctuations. This allows for estimating the corresponding log-likelihood as a function of interval size without presuming the fluctuations to be normally distributed, as is the case in conventional DFA. We demonstrate the validity and robustness of our algorithm using a variety of simulated signals, ranging from scale-free fluctuations with known Hurst exponents, via more conventional dynamical systems resembling exponentially correlated fluctuations, to a toy model of neural mass activity. We also illustrate its use for encephalographic signals. We further discuss confounding factors like the finite signal size. Our model comparison provides a proper means to identify power-law scaling including the range over which it is present.
authors.affiliation: MOVE Research Institute, Department of Human Movement Sciences, VU Amsterdam, The Netherlands; Center for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, Roc Boronat 138, Barcelona 08018, Spain.
authors.forename: Robert
authors.initials: R
authors.lastname: Ton
authors.affiliation: MOVE Research Institute, Department of Human Movement Sciences, VU Amsterdam, The Netherlands.
authors.forename: Andreas
authors.initials: A
authors.lastname: Daffertshofer
mesh_terms: D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D008959:Models, Neurological; D015233:Models, Statistical
keywords: DFA; Model selection; Power law