学步园

Judges’Commentary:

TheOutstanding Geographic

ProfilingPapers

Marie Vanisko

Dept. ofMathematics, Engineering, and Computer Science

Carroll College

Helena, MT 59625

mvanisko@carroll.edu

Introduction

The stated problemthis year dealt with the issue of geographical profiling

in theinvestigation of serial criminals. International interest in this topic has

led to numerouspublications, many of which present mathematical models for

analyzing theproblems involved. Although it was entirely appropriate and

expected that teamsworking on this problem would review the literature on

the subject andlearn from their review, teams that simply presented published

schemes as theirmathematical models fell far short of what was expected. The

judges looked forsparks of creativity and carefully explained mathematical

model building withsensitivity analysis that went beyond what is found in the

literature. Thisfactor is what added value to a paper.

Documentationand Graphs

We observed anoticeable improvement in how references were identified

and in the specificprecision in documenting them within the papers. Consid-

ering the numerousonline resources available, proper documentation was an

especiallyimportant factor in this year’s problem.

Despite theimprovement, many papers contained charts and graphs from

Web sources with nodocumentation. All graphs and tables need labels and/or

legends, and theyshould provide information about what is referred to in the

paper. The bestpapers used graphs to help clarify their results and documented

trustworthyresources whenever used.

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The UMAP Journal 31.2 (2010)

Assumptions

In many cases,teams made tacit assumptions about the criminals being

considered but didnot state or justify critical mathematical assumptions that

were later usedimplicitly. Assumptions concerning probability distributions,

anchor points,distances, units, mathematical procedures, and how to measure

results weregenerally not discussed or justified.

Since this is amodeling contest, a lot of weight is put on whether or not the

model could beused, with modification, in the real world. Also, clear writing

and exposition isessential to motivate and explain assumptions and to derive

and test modelsbased on those assumptions.

Summary

The summary is ofcritical importance, especially in early judging. It should

motivate the readerand be polished with a good synopsis of key results. For

this problem, teamswere asked to add to their one-page summary (which can

have some technicaldetails) also a two-page executive summary appropriate

for the Chief ofPolice. Many teams seemed to assume that the Chief of Police

would haveimpressive mathematical credentials.

The Problemand Its Analysis

Teams were asked todevelop at least two different schemes for generating

geographicalprofiles and then to develop a technique for combining the results

of the differentschemes in such a way as to generate a useful prediction for law

enforcementofficers. Although the papers designated as Meritorious generally

developed interesting schemes, very few papers did an adequate job of testing

their results and doing sensitivity analysis.  

Most papers dealt with issues associated with the serial criminal’s home

base, usually referred to as the anchor point, and the buffer zone around that

point within whichthe criminal is unlikely to commit crimes. Locations were

identified using latitude and longitude and sometimes a time factor.
Weights

were frequently assigned to data points, sometimes taking more recent crimes

into account moreheavily and sometimes incorporating qualitative factors into

the scheme. Teams used various metrics in describing “distances” between the

anchor point andcrime locations. Papers that rose to the top
used well-defined

metrics that were clearly explained. One cannot measure the reliability or

validity of a model without clearly defined metrics.

Many teams mentioned that there was not a lot of data with which they could

validate their model, although they did find some specific location information

that included from13 to 20 crimes in a given series. Some teams used as their

only example theSutcliffe case cited in the problem. In almost all cases, teams