Calculating the geography of crime

A mathematician fine-tunes how to blend crime records, geography to track down serial criminals

WASHINGTON, D.C. — Math as a tool for tracking down criminals has never been as precise as the TV show Numb3rs depicts. But mathematicians are developing better ways to at least estimate where a person on a crime spree might live.

Using information about the layout of a city, such as the location of similar crimes during the past few years, beefed up mathematical tools could improve estimates of where a criminal lives based on where he or she commits crimes, according to new research presented January 7 at the annual Joint Mathematics Meetings.

“I feel like I’m in a gold mine and I’m the only one who knows what gold looks like,” says Mike O’Leary, an applied mathematician at Towson University in Maryland who performed the new research. “There are so many good mathematical problems in this field” of criminology.

A well established principle of criminology is that perpetrators will tend to commit more crimes close to their homes simply because of convenience and the realities of transportation. So older techniques estimate where a criminal lives based on the locations of a string of unsolved crimes that are all attributed to that criminal.

But those techniques ignore the actual geography of a city, assuming instead that the likelihood of a criminal striking near his or her home drops off evenly in all directions regardless of geography.

“They don’t have any way to incorporate yet data about geography,” O’Leary says. “Mathematically they just don’t have the tools for it.”

To find the perpetrator of a type of crime, such as robbing a convenience store, O’Leary’s methods would use historical records of incidences of similar crimes to generate a likelihood distribution for that crime for the whole city. This distribution inherently contains geographic information such as where the major roads are located and where easy targets are located. The analysis also folds in census data about neighborhood demographics, as well as a mathematical analysis of how far from home criminals of different ages typically strike. Younger criminals tend to commit crimes closer to home.

Other researchers have also developed software tools in recent years that attempt to incorporate geographic information. However, “Up until now the majority of the research has been done by social scientists such as myself,” comments Ned Levine, a geographical researcher at Ned Levine & Associates in Houston who developed crime-analysis software called CrimeStat. O’Leary has “added some insights into the mathematics that previously we were struggling with,” he says. “He’s really cleaning up the mathematics.”

At their best, such analyses, including O’Leary’s, are prone to error and only give police a starting point — perhaps for checking whether people previously convicted of the same crime live in the area identified by the techniques. O’Leary is working on computer software that performs his analysis. The code for the software will be made freely available, and the complete software package will be free for police departments to use.

“It’s a lot of fun,” O’Leary says. “I can’t wait until this goes and does something.”

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