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Anchoring

Anchoring the

the

the Geographic

Geographic

Geographic Pro

Pro

Pro 



 les

les

les of

of Serial

Serial

Criminals

Criminals by

by Clusters

Clusters

Clusters and

and

and Bayesian

Bayesian

Abstract

Since decades ago ,people have realized that there are important relationships between

geography and the series of crimes .And with the rapid development of science and

technology, t he study of serial crimes prediction has been a fruitful area of

mathematical research . This paper studies the different schemes to estimate the

location of the criminal

’

s residence and the technique to predict the possible locations

of the next cri me.

According to the request, we have to solve two main problems: one is to generate a

geographic profile of the offender's residence, the other is to generate a useful method

to predict the location of the next crime. In order to prove the accuracy of our method,

we also study the Peter Sutcliffe

’

s serial murder case .

For the first problem, we use two different schemes.

build the Cent er of Minim um

Distance Model to generate geographical profiling of the criminal

’

s residence based

on the least effort principle. After that we generate Bayesian Model based on Bayes

Theorem and get another geographical profiling.

For the second problem, we use the Bayesian Model to predict the location of the next

crime based on the predicted residence and the locations of committed crimes.To

make our method more accurate, we introduce Cluster Analysis to divide all the crime

sites into 4 groups.To obtain the prediction of every group ,we apply the method

which is also used in the combination of two schemes in the first problem.

Finally, we write an executive summary to the chief of police providing police

providing a broad overview of the potential issues and our approach.

Contents

Summary ............................................................................................. . 1

1 Introduction

Introduction

Introduction ....................................................................................3

1.1 Background ...................................................................................... 3

1.2Geographic Profiling ............................................................................. 3

1.3Objectives ........................................................................................... 3

2 Center

Center

Center of

of Minimum

Minimum

Minimum Distance

Distance

Distance Model

Model

Model . ............................................. 5

2.1 Assumptions ....................................................................................... 5

2.2 Notations ........................................................................................... 6

2.3 Center of Minimum Distance Model ....................................................... 6

2.4 Distance-decay Model.. ........................................................................ . 6

2. 5 Case Study ......................................................................................... 6

3 Bayesian

Bayesian

Bayesian Model

Model

Model ... ............................................................................ 8

3 . 1 Assumptions ....................................................................................... 8

3 . 2 Notations and Definitions .................................................................... 8

3 .3 Bayesian Model ................................................................................. . 9

3 .4 Simple Models for O ff ender Behaviour ................................................... . 9

3 .5 Case Study ........................................................................................ . 10

3.6 Validation of Prediction .................................................................. ...... 10

4 Combination

Combination

Combination of

of the

the

the Results

Results

Results of

of the

the

the Two

Two

Two Schemes

Schemes

Schemes ......................... ... 11

5 Prediction

Prediction

Prediction of

of the

the

the Next

Next Crime

Crime

Crime .......................................................... . 11

5 .1 Initial Prediction Method ..................................................................... . 11

5 .2 Developed Prediction Method ............................................................... . 11

5.3 Validation of Prediction ......................................................................... 15

6 Executive

Executive

Executive Summary

Summary

Summary ..................................................................... . ..15

6 .1 Overview: Strengths and Weaknesses of th e Model .................................... 15

6 .2 Internal Workings of the Model . .............................................................. 15

6.3 Future Considerations .............. .............................................................. 16

6 .3 Recommendations ................................................................................. 16

References

References ................................................................................. ......... 17

1 Introduction

Introduction

1. 1

1 Background

Background

During the 5 years from 1975 to 1980, Peter William Sutcliffe, who was also

dubbed The Yorkshire Ripper, murdered thirteen women and subjected a number of

other people to vicious attacks [1] .As we all know,the Serial crime has become a

serious problem in society , causing the panic of quite a lot people. T herefore,it has

become an important issue to avoid another victim by analysing the crimes committed

before.

number of sophisticated techniques have been developed to generate a

useful prediction for law enforcement officers based on the time and locations of the

past crime scenes, such as the “

“

“ center of a mass ”

”

” method .In 1980 Peter Sutcliffe

convicted of thirteen murders and subjecting a number of other people to vicious

attacks. One of the methods used to narrow the search for Mr. Sutcliffe was that so

called “ center of mass ” method . Thus, D.Kim Rossmo advanced a new criminal

investigative methodology called "Geo-graphic Profiling" in 2000 [2] .

1.2

1.2 Geographic

Geographic

Geographic profiling

profiling

Geographic profiling is a criminal investigative methodology that analyzes the

locations of a connected series of crimes to determine the most probable area of

offender residence. Typically used in cases of serial murder or rape. the technique

helps police detectives prioritize information in large-scale major crime investigations

that often involve hundreds or thousands of suspects and tips.

While it may not seem so, understanding an offender

’

s geographical tendencies and

habits can tell investigators and profilers a great deal about the personality of that

individual. Geographical profiling is growing in popularity and, combined with

offender profiling, is a very helpful tool in the investigation process of a serial murder

case. [

[

[ 3

3 ].

1.3

1.3 Objectives

Objectives

Our goal is to develop at least two different schemes to generate a geographical

profile. After that, we will develop a technique to combine the results of the different

schemes and generate a useful prediction. Our prediction will provide some kind of

estimate or guidance about possible locations of the next crime based on the time and

locations of the past crime scenes. What

’

s more, we will show how reliable the

estimate will be in a given situation according to our model.

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liangyuxuan0617

2014-08-28

不是原题。。。是论文

喜多

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