Santa Fe Institute

Statistical analysis that fits the crime

Sept. 28, 2012 10:13 a.m.

While many urban indicators -- infrastructure, wages, patents, etc. -- are known to scale predictably with city population, previous statistical analyses of cities have not examined in detail how year-to-year deviations in certain highly variable, lower frequency statistics fit with these general expectations.

Serious crime, such the number of homicides, is especially problematic for scientists study- ing urban dynamics because crime rates for an individual city can vary drastically from year to year. One year a city might experience a single homicide, and the next year, perhaps five. A peaceful year with no crimes is a particularly knotty statistical problem because for scaling purposes, a zero crime rate can be expected only for a city of zero population.

In a recent paper, three researchers demonstrate an analysis method that -- for the first time, they believe -- resolves these statistical difficulties and, using homicide data from three nations with very high but rapidly changing rates of violent crime -- Brazil, Colombia, and Mexico -- fit real-world data to their method.

The paper, “The Statistics of Urban Scaling and Their Connection to Zipf’s Law,” by Andres Gomez-Lievano, SFI Postdoctoral Fellow HyeJin Youn, and SFI Professor Luis Bettencourt, was published in PLoS One on July 18, 2012.

“The main issue with studying homicides and other violent crimes is that numbers are usually -- and fortunately -- small, and vary significantly from year to year,” says Bettencourt. “Crime is almost always measured as a per capita rate, usually a small number per 100,000 people, which doesn’t reveal much underlying truth about variations in crime between cities and over time.”

Additionally, notes Gomez-Lievano, a graduate student at Arizona State University, scaling analyses are usually applied to large cities; the team wanted to extend the analyses to cities of all sizes, including very small ones. Applying simple scaling laws to all cities, however, typically generates false conclusions, especially with data from small places where zeroes are more probable. Their new statistical framework corrects this shortcoming.

Their work shows that although population is a poor one-for-one predictor of homicide rates, homicides are, indeed, statistically entangled with population size. Moreover, they show that when using their statistical method, the distribution of homicides is much more predictable than previously believed.

“The deeper level of understanding made possible with our new method might, if considered by policy makers, contribute to making real progress in fighting crime, especially in taking into account its variability and helping unveil its underlying dynamics” says Bettencourt.

Next the researchers plan to use data from many urban systems around the world to examine how crime rates and their statistics evolve over time, and shed light on successful strategies to fight crime and detect impending crime waves.

Read the paper in PLoS One (July 18, 2012)

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