Power-laws, scaling laws, and other statistical laws play a fundamental role in the study of complex systems. They are typically interpreted as an emerging feature of the system and serve as a motivation for the proposal of mechanistic models that aim to reproduce them. In this talk I will review and critically analyse the role played by statistical laws in complex systems. In particular, I will argue that traditional statistical methods used to test and validate these laws are not suitable because (i) they are not based on a generative process of the data and thus do not test the mechanistic models; and (ii) they rely on the assumption of independent observations and focus on fixed parameters (not family of distributions). I will then propose solutions to this problem by introducing methods that account for correlations and other constraints in the data [1,3] and by incorporating mechanistic generative models into the statistical analysis [2]. I will discuss linguistic laws of word frequency, extreme-event distributions, and urban scaling laws.
References:
[1] J. M. Moore, G. Yan, E. G Altmann "Nonparametric Power-Law Surrogates" , Phys. Rev. X 12, 021056 (2022)
[2] E. G. Altmann "Spatial interactions in urban scaling laws", PLOS ONE 15, e0243390 (2020)
[3] M. Gerlach and E. G. Altmann, "Testing statistical laws in complex systems", Phys. Rev. Lett. 122, 168301 (2019)
