Dresden 2017 – wissenschaftliches Programm

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 15: Focus Session: Cities as complex systems

SOE 15.6: Vortrag

Mittwoch, 22. März 2017, 16:15–16:30, GÖR 226

Statistical issues in scaling laws’ estimation — •Jose M. Miotto¹, Jorge C. Leitão², Martin Gerlach³, and Eduardo G. Altmann⁴ — ¹Max-Planck-Institut für Physik komplexer Systeme, Dresden, Germany — ²iCourts, University of Copenhagen, Copenhagen, Denmark — ³Department of Chemical and Biological Engineering, Northwestern University, Chicago, USA — ⁴School of Mathematics and Statistics, University of Sydney, Sydney, Australia

One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g. patents) scale nonlinearly with the population x of the cities in which they appear, i.e. y∼ x^β, β≠1. More recently, the generality of this finding has been questioned in studies that used new databases and different definitions of city boundaries. We investigated the existence of nonlinear scaling, using a probabilistic framework in which fluctuations are accounted for explicitly. In particular, we show that this allows not only to (i) estimate β and confidence intervals, but also to (ii) quantify the evidence in favour of β≠1 and (iii) test the hypothesis that the observations are compatible with the nonlinear scaling. We employ this framework to compare five different models to 15 different datasets and we find that the answers to points (i)*(iii) crucially depend on the fluctuations contained in the data, on how they are modelled, and on the fact that the city sizes are heavy-tailed distributed.