Bayesian Geographic Profiling: A Fundamental Limitation

Abstract

Geographic profiling is a criminal investigative technique that analyzes the locations of a crime series to determine the most probable area of offender residence. Police agencies employ the methodology for suspect prioritization and information management purposes in serial crime cases. Geoprofiles are probability maps generated by an algorithm that integrates distance decay functions originating from the point pattern of the connected crime sites. A more recent approach, known as empirical Bayes journey-to-crime estimation (or Bayesian geographic profiling), seeks to supplement these models with area-based historical offender and crime data. Spatial information from previous crime trips is used to calibrate analyses following the assumption that the unknown offender likely resides in the same neighborhood as past criminals who offended in the location of the new crime series. Inferring individual suspect rankings from historical area rankings, however, creates an ecological fallacy, and the greater the congruence between past offenders and future suspects, the more tautological the analysis. Although Bayesian models cannot be used to inform suspect prioritization—the main function of geographic profiling—the approach could have applicability for police strategies based on area prioritization. Surprisingly, this major limitation of the Bayes approach to geoprofiling has been ignored in the literature.

地理画像是一种犯罪调查技术, 它分析某犯罪序列的各个位置, 确定罪犯最可能居住的区域。在连续犯罪案件中, 警察部门采用该方法对犯罪嫌疑人进行优先排序以及信息管理。地理画像算法集成了基于犯罪位置点模式的多个距离衰减函数, 并由算法生成概率地图。最新的方法是经验贝叶斯犯罪出行估计（贝叶斯地理画像）, 旨在用区域历史罪犯和犯罪数据对模型进行补充。假设新案发点的未知罪犯和过往罪犯可能居住在同一社区, 过往犯罪出行的空间信息可用于校正分析。然而, 根据历史区域排序去推断犯罪嫌疑人排序, 会产生层次谬误, 过往罪犯和未来犯罪嫌疑人之间的一致性越大, 分析的重复度就越高。虽然贝叶斯模型不能用于犯罪嫌疑人的优先排序（这是地理画像的主要功能）, 但可用于基于区域优先排序的警察策略。令人惊讶的是, 贝叶斯在地理画像中的这个主要局限在文献中被忽略了。

La construcción de perfiles geográficos es una técnica de investigación criminal que analiza las características locacionales de una serie de delitos para establecer el área más probable de residencia del delincuente. Las agencias policiales utilizan esta metodología para priorizar a los sospechosos y con el propósito de gestionar la información en los casos de crímenes en serie. Los geoperfiles son mapas de probabilidad generados por un algoritmo que integra funciones de declinación de la distancia originadas por el patrón de puntos de las escenas del crimen conectadas. Un enfoque más reciente, conocido como estimación empírica del viaje hasta la escena del crimen de Bayes (o perfiles geográficos bayesianos), busca complementar estos modelos con datos históricos del criminal basados en área. La información espacial de los desplazamientos anteriores de la delincuencia se usa para calibrar análisis, siguiendo el supuesto de que el delincuente desconocido probablemente reside en el mismo barrio que los delincuentes anteriores que delinquieron en la ubicación de la nueva serie de delitos. No obstante, inferir la categorización individual de sospechosos desde las clasificaciones históricas por área crea una falacia ecológica, y entre más grande sea la congruencia entre los delincuentes anteriores y los futuros sospechosos, más tautológico llegará a ser el análisis. Aunque los modelos bayesianos no pueden usarse para informar la priorización de los sospechosos –la función principal de la construcción de perfiles geográficos– el enfoque podría ofrecer aplicabilidad en las estrategia policiales basadas en la priorización por área. Sorprendentemente, esta limitación importante del enfoque de Bayes para la producción de geoperfiles ha sido ignorada en la literatura.

Key Words:

• Bayesian analysis
• criminal investigations
• geographic profiling

关键词:

• 贝叶斯分析
• 犯罪调查
• 地理画像

Palabras clave:

• análisis bayesiano
• elaboración de perfiles geográficos
• investigaciones criminales

Notes

1 For some reason, these are referred to as risk surfaces.

2 A number of these studies analyzed the same crime data from Baltimore County and therefore fail to provide independent replication. More problematic is the geographic context; the City of Baltimore, which has a much higher crime rate than Baltimore County, is surrounded on all three of its land borders by the county. What effect this unusual horseshoe configuration has on the county’s spatial crime patterns, particularly offender crime trips, has not been studied.

3 Goodwill, van der Kemp, and Winter (2013) proposed adding numerous information sources to a geographic profile but failed to evaluate either their feasibility or utility. Many of their ideas would be highly resource intensive (analyzing all purchase receipts from every store, identifying all joggers and dog walkers near every crime site). Some ignore the legal prerequisites for police searches; geographic proximity does not provide the necessary grounds for a search warrant to obtain medical records, for instance. Other proposals are unlikely to produce much of value (reviewing library cards). The goal of geographic profiling is to help find the needle in the haystack, not to add more straw.

4 Subjects were asked the probability that a taxicab involved in a hit-and-run accident was blue, given that an eyewitness reported the cab was blue, but the city had many more green than blue taxicabs. Most subjects overestimated the blue probability. Tversky and Kahneman (1982) called this the representativeness heuristic.

Additional information

Notes on contributors

D. Kim Rossmo

D. KIM ROSSMO is a Professor in the School of Criminal Justice and Criminology and the Director of the Center for Geospatial Intelligence and Investigation, Texas State University, San Marcos, TX 78666. E-mail: [email protected]. His research interests include the geography of crime, environmental criminology, police investigations, criminal investigative failures, and offender profiling.