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Catching Lightning in a
Bottle: Forescasting
Next Events
Catching Lightning in a
Bottle: Forescasting
Next Events
Presented by
Dr. Derek J. PaulsenDirector, Institute for the Spatial Analysis of Crime
Assistant ProfessorEastern Kentucky University
2005 iPSY Conference
Presented by
Dr. Derek J. PaulsenDirector, Institute for the Spatial Analysis of Crime
Assistant ProfessorEastern Kentucky University
2005 iPSY Conference
Evolution of Crime Analysis in the U.S.
Increasing focus on Tactical Analysis and assistance in major crime investigations.
Increasing use of advanced technology Geographic profiling
Crime Series Identification software
Forecasting/Prediction
Great potential to assist in investigations, but research has been limited.
Developing Crime Series Analysis tools and training as part of a NIJ grant.
Evolution of Crime Analysis in the U.S.
Increasing focus on Tactical Analysis and assistance in major crime investigations.
Increasing use of advanced technology Geographic profiling
Crime Series Identification software
Forecasting/Prediction
Great potential to assist in investigations, but research has been limited.
Developing Crime Series Analysis tools and training as part of a NIJ grant.
Spatial Forecasting and Crime Analysis
Spatial Forecasting and Crime Analysis
Main Research QuestionsMain Research Questions
How accurate are traditional strategies in comparison to TWKDI at predicting the location of a future crime event in an active crime series?
Under what circumstances do forecasting techniques work?
Are there crime types that are better for forecasting than others?
What case specifics best predict success?
How accurate are traditional strategies in comparison to TWKDI at predicting the location of a future crime event in an active crime series?
Under what circumstances do forecasting techniques work?
Are there crime types that are better for forecasting than others?
What case specifics best predict success?
Forecasting Strategies Studied
Forecasting Strategies Studied
Traditional Methods
Standard Deviation Rectangles: “Gottleib Rectangles”
Jennrich/Turner Ellipse
Minimum-Convex-Hull Polygon
New Methods
Modified Correlated Walk Analysis
Time-Weighted Kernel Density Interpolation
Control Method
Modified Center of Minimum Distance
Traditional Methods
Standard Deviation Rectangles: “Gottleib Rectangles”
Jennrich/Turner Ellipse
Minimum-Convex-Hull Polygon
New Methods
Modified Correlated Walk Analysis
Time-Weighted Kernel Density Interpolation
Control Method
Modified Center of Minimum Distance
Standard
Deviation
Rectangle
Standard
Deviation
Rectangle
2 Standard Deviation rectangle around the mean center of the incident locations in the series
2 Standard Deviation rectangle around the mean center of the incident locations in the series
Jennrich-Turner Ellipse
Jennrich-Turner Ellipse
2 Standard Deviation ellipse based around the mean center of the incident locations in the series
and drawn around a least squares trend line
2 Standard Deviation ellipse based around the mean center of the incident locations in the series
and drawn around a least squares trend line
Mini
mum
Convex-Hull
Polygon
Mini
mum
Convex-Hull
Polygon
Creates a minimum bounding polygon around all of the incident locations in the series
Creates a minimum bounding polygon around all of the incident locations in the series
Modified
Correlated
Walk
Analysis
Modified
Correlated
Walk
Analysis
Uses the CWA as a seed point and creates a search area by drawing a circle with a radius of the
average distance between crime events in the series.
Uses the CWA as a seed point and creates a search area by drawing a circle with a radius of the
average distance between crime events in the series.
Ti
me-Weighted
Kernel
Density Interpolation
Ti
me-Weighted
Kernel
Density Interpolation
Kernel Density Interpolation of crime incident locations using time as a weighting variableKernel Density Interpolation of crime incident locations using time as a weighting variable
Modified
Center of
Mini
mum
Distance
Modified
Center of
Mini
mum
Distance
Uses the CMD as a seed point and creates a search area by drawing a circle with a radius of the average distance between crime events in the series.
Uses the CMD as a seed point and creates a search area by drawing a circle with a radius of the average distance between crime events in the series.
Data Used in StudyData Used in Study
247 serial crime events that occurred in Baltimore County, MD between 1994-1997.
Random sample of 45 cases in which there were 6 or more incidents.
Series ranged from 6-14 events
Burglary, Robbery, Arson, Auto theft, Rape, Theft
Last Crime was removed from series and remaining crimes were used to predict the final event.
Analysis was conducted using:
Arcview 3.3 and 9.0
Crimestat 2.0
Animal Movement Extension/CASE Program
247 serial crime events that occurred in Baltimore County, MD between 1994-1997.
Random sample of 45 cases in which there were 6 or more incidents.
Series ranged from 6-14 events
Burglary, Robbery, Arson, Auto theft, Rape, Theft
Last Crime was removed from series and remaining crimes were used to predict the final event.
Analysis was conducted using:
Arcview 3.3 and 9.0
Crimestat 2.0
Animal Movement Extension/CASE Program
Measuring Accuracy of Predictions
Measuring Accuracy of Predictions
How do you measure accuracy in predicting next events in a crime series?
Accuracy in prediction needs to encompass both correctness and the precision of the prediction in order to maintain practical utility.
A prediction may be accurate, but the predicted area may so large as to provide little practical benefit.
Methods
1. Correct: Was the final event location within predicted area.
2. Search Area: Average size of the predicted area.
3. Search Cost: Percent of base search area covered by the final predicted area.
4. Accuracy Precision: % of correct forecasts divided by the average predicted area.
How do you measure accuracy in predicting next events in a crime series?
Accuracy in prediction needs to encompass both correctness and the precision of the prediction in order to maintain practical utility.
A prediction may be accurate, but the predicted area may so large as to provide little practical benefit.
Methods
1. Correct: Was the final event location within predicted area.
2. Search Area: Average size of the predicted area.
3. Search Cost: Percent of base search area covered by the final predicted area.
4. Accuracy Precision: % of correct forecasts divided by the average predicted area.
Search Area, Search Cost, and Accuracy Precision
Search Area, Search Cost, and Accuracy Precision
Method % CorrectAvg.
Search Area
Avg. Search Cost
Accuracy Precision
SDR 80% 151.68 170% .5274
JTE 73% 122.10 134% .5978
MCP 42% 23.21 26% 1.8095
CWA 24% 59.82 85% .4012
TWKDI 52% 19.35 21% 2.6873
CMD 80% 59.82 85% 1.3373
Average base search area was 92 sq. milesAverage base search area was 92 sq. miles
Success by crimes in seriesSuccess by crimes in series
0
20
40
60
80
100
120
4 5 6 7 8 9 10 11 12 13
Number of Crimes
Percent Correct
SuccessPoly. (Success)
0
20
40
60
80
100
120
4 5 6 7 8 9 10 11 12 13
Number of Crimes
Percent Correct
SuccessPoly. (Success)
Average: 57%
Average: 57%
Average distance between crimes
Average distance between crimes
0
1
2
3
4
5
6
7
4 5 6 7 8 9 10 11 12 13
Number of Crimes
Average distance in miles
SuccessFailure
Dispersion by Crime in series
Dispersion by Crime in series
02468
101214161820
4 5 6 7 8 9 10 11 12 13
Number of Crimes
Average Disperison in Miles
SuccessFailure
Search Area size by number of crimes in series
Search Area size by number of crimes in series
0
1
2
3
4
5
6
4 5 6 7 8 9 10 11 12 13
Number of crimes
Average Search Area (miles)
SuccessFailure
Accuracy/Precision by crime number
Accuracy/Precision by crime number
0
10
20
30
40
50
60
4 5 6 7 8 9 10 11 12 13
Number of Crimes
Accuracy/Precision Ratio
AP RatioPoly. (AP Ratio)
Commercial Burglary Series
Commercial Burglary Series
-5 crimes within 6 days.
-Stealing cigarettes from gas stations
-Crime area of approximately 10 square miles
-Over 409 businesses within the area.
-5 crimes within 6 days.
-Stealing cigarettes from gas stations
-Crime area of approximately 10 square miles
-Over 409 businesses within the area.
Commercial Burglary Series
Commercial Burglary Series
-8 gas stations within initial crime area
-22 gas stations within area and 1/2 miles surrounding it.
-8 gas stations within initial crime area
-22 gas stations within area and 1/2 miles surrounding it.
Commercial Burglary Series
Commercial Burglary Series
-Prioritized search into two main areas of .9 square miles
-Top area contained 3 gas stations
-Second tier area contained 3 gas stations
-Prioritized search into two main areas of .9 square miles
-Top area contained 3 gas stations
-Second tier area contained 3 gas stations
Commercial Burglary Series
Commercial Burglary Series
-Last station burglarized was within top priority search area.
-Last station burglarized was within top priority search area.
Overall FindingsOverall Findings
Time-Weighted is the best at reducing the search area while remaining accurate.
Success most influenced by number of incidents in series and the distribution of the crimes.
Convex-Hull Polygon and modified CMD also produced good results, whereas other traditional strategies were poor performers.
While average predicted areas are rather large, practical use could reduce them to smaller area.
Time-Weighted is the best at reducing the search area while remaining accurate.
Success most influenced by number of incidents in series and the distribution of the crimes.
Convex-Hull Polygon and modified CMD also produced good results, whereas other traditional strategies were poor performers.
While average predicted areas are rather large, practical use could reduce them to smaller area.
Future IssuesFuture Issues
More research, more data.
Determine impact of other factors such as crime type, city type, and road network.
Determine case variables that may indicate predictive success.
Develop and analyze other new strategies.
Temporal as well as spatial forecasting/prediction
More research on serial offender spatial and temporal behavior.
More research, more data.
Determine impact of other factors such as crime type, city type, and road network.
Determine case variables that may indicate predictive success.
Develop and analyze other new strategies.
Temporal as well as spatial forecasting/prediction
More research on serial offender spatial and temporal behavior.
Data or
Suggestions?
Data or
Suggestions?
Contact Information:
Dr. Derek J. PaulsenAssistant Professor
Director, Institute for the Spatial Analysis of Crime
Eastern Kentucky UniversityRichmond, KY USA 40507-3102
Contact Information:
Dr. Derek J. PaulsenAssistant Professor
Director, Institute for the Spatial Analysis of Crime
Eastern Kentucky UniversityRichmond, KY USA 40507-3102
