2010年MCM犯罪学问题评审commentary

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

used their model to predict the location of the final crime based on all of the

previous locationsfor that criminal. They could easily have had many more

data points withwhich to validate their models. For example, if 13 crime

locations wereavailable, they could have used the first nlocations to predict

the location ofcrime n + 1, for each n = 7, . . . , 12. The judges agreed that this

problem did not lend itself to validation by simulation, as many other problems

do.

In describing thereliability of predicted results for proposed models, it

was sometimesdifficult to determine precisely how teams had arrived at their

results. Since theliterature is full of models and even computer models, it

would have beenworthy if teams had solved a problem via one of these meth-

ods and used thatas a baseline to compare the results of original models that

they proposed. Nota single team did this to the judge’s satisfaction. Judges

do not generallylook for computer code, but they definitely look for precise

algorithms thatproduce results based on a given model.

 

 

ConcludingRemarks

 

Mathematicalmodeling is an art. It is an art that requires considerable skill

and practice inorder to develop proficiency. The big problems that we face

now and in thefuture will be solved in large part by those with the talent,

the insight, andthe will to model these real-world problems and continuously

refine those models.Surely the issue of solving crimes involving serial killers

is an importantchallenge that we face.

The judges are veryproud of all participants in this Mathematical Contest

in Modeling and wecommend you for your hard work and dedication.

 

 

About theAuthor

 

Marie Vanisko is aMathematics Professor Emerita from Carroll College

in Helena, Montana,where she taught for more than 30 years. She was also a

Visiting Professorat the U.S. Military Academy at West Point and taught for five

years at CaliforniaState University Stanislaus. In both California and Montana,

she directed MAATensor Foundation grants on mathematical modeling for

high school girls.She also directs a mathematical modeling project for Montana

high school andcollege mathematics and science teachers through the Montana

Learning Center atCanyon Ferry, where she chairs the Board of Directors. She

has served as a judge for both the MCM and HiMCM.