https://doi.org/10.1140/epjds/s13688-026-00658-x
Research
Decoding the city: multiscale spatial information in urban income distributions
1
Dept. of Ecology and Evolution, Dept. Sociology, University of Chicago, 60637, Chicago, IL, USA
2
Santa Fe Institute, 87501, Santa Fe, NM, USA
3
Vienna Complexity Science Hub, 1030, Vienna, Austria
4
Institute for New Economic Thinking at the Martin School, University of Oxford, OX1 3UQ, Oxford, UK
5
School of Sustainability, College of Global Futures, Arizona State University, 85281, Tempe, AZ, USA
a
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Received:
22
September
2025
Accepted:
16
April
2026
Published online:
30
April
2026
Abstract
Cities are characterized by the coexistence of general aggregate patterns, along with many local variations. This poses challenges for analyses of urban phenomena, which tend to be either too aggregated or too local, depending on the disciplinary approach. Here, we use methods from statistical learning theory to develop a general methodology for quantifying how much information is encoded in the spatial structure of cities at different scales. We illustrate the approach via the multiscale analysis of income distributions in over 900 US metropolitan areas. By treating the formation of diverse neighborhoods as a process of spatial selection, we quantify the complexity of explanation needed to account for personal income heterogeneity observed across all US urban areas and each of their neighborhoods. We find that spatial selection is strongly dependent on income levels with richer and poorer households appearing spatially more segregated than middle-income groups. We also find that different neighborhoods present different degrees of income specificity and inequality, motivating analysis and theory beyond averages. Our findings emphasize the importance of multiscalar statistical methods that both coarse-grain and fine-grain data to bridge local to global theories of cities and other complex systems.
Key words: Bayesian statistics / Spatial selection / Neighborhood effects / Income
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjds/s13688-026-00658-x.
Handling Editor: Efrat Blumenfeld Lieberthal
© The Author(s) 2026
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