For the second problem, using Rayleigh distribution function, we obtain a preliminary probability distribution of the crime site based on the residence determined in the first problem . Taking geographical character and the offender’s geographical preference into account, we utilize cluster analysis to divide all the crime sites into 4 zones. In these 4 zones, we construct 4 two-dimensional normal distributions around the 4 circle centers with the standard deviations being the radii of the circles. In view of the influence of the crime time, we add a time factor to the preliminary distribution. As a result, the preliminary distribution is modulated by geographical and temporal factors, producing an ultimate prediction, which is rather satisfactory after validation.
3 Center of Minimum Distance Model.................................. 5
3.1 Notations ........................................................................ 5 3.2 Simplifying Assumptions.................................................... 6 3.3 Center of Minimum Distance Model ..................................... 6 3.4 Case Study....................................................................... 6
7 Validation of Prediction...................................................... 20 8 Evaluating of Solutions ....................................................Chief of Police ........................ 22
9.1 Preparatory Work.............................................................. 22 9.2 Overview of the Potential Issues........................................... 22 9.3 Suggestion ....................................................................... 23
For the first problem, based on the least effort principle, we build the Center of Minimum Distance Model and obtain the possible residence area of the criminal. Then based on Bayes’ Theorem and Rayleigh distribution function, we build the Bayesian Model and get another possible residence area. After that, we design a technique of using a minimum circle to cover the two areas to combine the two schemes.
2 Problem Analysis ............................................................... 4
2.1 Overall Strategy ................................................................ 4 2.2 The Strategies for Problem I................................................. 4 2.3 The Strategy for Problem II ................................................. 4
8.1 Strengths ......................................................................... 20 8.2 Weaknesses...................................................................... 21 8.3 Future Consideration ......................................................... 21
References ................................................................................. 24
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Team #7120
page3 of 24
1 Introduction
1.1 Background
Serial crimes have a serious effect on people’s lives and continuously challenge people’s baseline of morality. Thus, how to arrest the criminals before he or she commits another crime becomes an important issue. A 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.
1.1 Background ..................................................................... 3 1.2 Geographic Profiling.......................................................... 3 1.3 Objectives........................................................................ 3
4 Bayesian Model .................................................................. 9
4.1 Notations and Definitions ................................................... 9 4.2 Simplifying Assumptions.................................................... 10 4.3 Bayesian Model ................................................................ 10 4.4 Case Study....................................................................... 12 4.5 The Discussion of α............................................................ 12
Finally, an executive summary is presented for law enforcement officers.
Contents
Summary ................................................................................... 1 1 Introduction ....................................................................... 3
5 Combination of the Results of the Two Schemes................ 13 6 Prediction of the Next Crime.............................................. 14