Efficient computational testing of scale-free behavior in real-world systems

Abstract With big data becoming available across the physical, life and social sciences, researchers are turning their attention to the question of whether universal statistical signatures emerge across systems. Power-laws are a particularly potent example, since they indicate scale-free or scale invariant behavior and are observed in physical systems near phase transitions. However, the same scale-free property that enables them to unify behaviors across multiple spatiotemporal scales, also means that usual Gaussian-based approaches cannot be used to test their presence. Here we analyze the crucial question of how to implement a power-law test efficiently, given that a key part involves multiple Monte Carlo simulations to obtain an accurate statistical p-value. We present such a computational scheme in detail.

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