Model selection for identifying power-law scaling

TL;DR

This paper introduces a Bayesian model comparison algorithm based on DFA to accurately identify and quantify power-law scaling in neural signals, addressing limitations of traditional methods.

Contribution

The authors develop a novel algorithm that improves power-law detection in neural data by using Bayesian model comparison with DFA, accounting for non-normal fluctuations and finite data effects.

Findings

Algorithm accurately detects power-law scaling in simulated signals.

Robustly distinguishes power-law from alternative models.

Effective on real encephalographic data.

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.