Aoristic crime analysis
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One of the problems which can be encountered when analysing crime data is the problem of temporal inaccuracy. This is usually because the actual time (and occasionally the date) of the incident is unknown to the victim. If a burglary victim is away on holiday, the start time and end time of the crime might be weeks apart! With the inherent inaccuracy of the source data, it is not surprising therefore that this temporal aspect of crime analysis has received less attention in the academic world. Within the police service, although active police officers often know where crime is concentrated, they may not necessarily know when it is happening with any accuracy, nor whether the localised crime rate is rising or falling.
The main problem is that the victim of a burglary or motor vehicle crime does not know exactly when the crime occurred. This is less often the case with crimes like assault (it tends to be something you notice immediately!) but can hamper the accurate analysis of high volume crime. There are a number of different ways you can resolve the problem.
You could employ a RIGID search and search your crime data for those crimes which definitely happened in the search period. For example, if you were only looking for crimes that happened overnight, you might search your crime database for everything that happened between 6pm and 6am. This would exclude crimes that occurred between 5pm and 7pm because they might have occurred before your search.
You could AVERAGE each crimes from and to times (and/or dates) and use the mean of the timeline as the search point. This method is easy to calculate but lacks accuracy. After all, who is to say that the crime happened in exactly the middle of the timeline?
An alternative to these two is to employ an AORISTIC search which considers all records which might have occurred within the search criteria time. Aoristic is defined in the Shorter Oxford English Dictionary as "without defined occurrence in time".
FREQUENTLY ASKED QUESTION: "Why Aoristic?"
ANSWER: When Michael McCullagh and I submitted a paper to a journal, we originally had the term 'spatio-temporal', as we were dealing with crime committed at a specific location but with an unspecific time. The reviewers of the journal accepted the paper on the condition that we change the term away from 'spatio-temporal' as that (apparently) has a particular meaning within GIS. Hence we were forced to find another term!
FREQUENTLY ASKED QUESTION: "What does Aoristic mean?"
ANSWER: Aoristic is from the Greek term Aorist, defined in the Shorter Oxford English Dictionary as "without defined occurrence in time".
The aoristic temporal process is summarised in the diagram. Horizontal bars represent crime incidents which have a start time, a time span (the length of the bar) and an end time. The search criteria similarly has a start and end time shown by the vertical blue arrows. The small red markers in the middle of each event represent the location of the average along the time line. One of the limitations of the averaging methods is visible in the second incident from the top. Although a considerable amount of the second incident takes place within the search parameters, it is not included because the location of the average is just outside the search criteria. Averaging the date field has been used in studies of burglary repeat victimisation, and although computationally simple and an adequate solution for the longer time periods of repeat victimisation studies, this is a compromise answer. It ties the event time to one possible time which, although the mean of the possible event times, is no likelier than any other time. A search based on fixed temporal windows adds emphasis to only one search period and denies the incident the chance to register with other equally applicable categories.
For further details of this process with a spatial application, see:
Ratcliffe, J.H. (2002) Aoristic signatures and the spatio-temporal analysis of high volume crime patterns
Journal of Quantitive Criminology, 2002, Volume 18 Issue 1: 23-43. The paper can be downloaded here.