Detecting and Preventing Emerging Outbreaks of Crime

1
Detecting and Preventing Emerging Outbreaks of
Crime Daniel B. Neill Carnegie Mellon
University Heinz School of Public Policy E-mail
neill_at_cs.cmu.edu
Joint work with Wilpen Gorr (Heinz School, CMU).
This work was partially supported by NSF grant
IIS-0325581 and CDC grant 1 R01 PH000028-01.
2
Crime surveillance
Crime prevention is an important aspect of public
health, yet has received relatively little
attention.
Crime can contribute both directly and indirectly
to adverse health effects, and also impacts
the overall happiness and well-being of a
community.
Goals of crime surveillance To help local police
departments to rapidly detect and respond to
emerging patterns of crime. To predict crime
patterns in advance, allowing departments to
allocate extra resources and carry out other
interventions to prevent crime.
3
Crime surveillance
Many parallels exist between the domains of
crime surveillance and disease surveillance.
In particular, geographic surveillance methods
have become increasingly important in law
enforcement.
New methods for crime hot-spot detection using
electronic case reports have increased
situational awareness and enabled more rapid
police response to emerging high-crime areas.
Screen shot from our spatial disease surveillance
software.
Crime map of San Diego, with detected hot-spot
4
Crime surveillance
Many parallels exist between the domains of
crime surveillance and disease surveillance.
In particular, geographic surveillance methods
have become increasingly important in law
enforcement.
Recent work in crime forecasting has enabled law
enforcement officials to predict and prevent
rises in crime using a variety of leading
indicator data.
Screen shot from our spatial disease surveillance
software.
Crime map of San Diego, with detected hot-spot
5
Challenges of crime surveillance
Current methods for crime detection and
forecasting partition the surveillance area into
multiple non-overlapping regions, and perform
time series analysis for each region.
Because the number of serious crimes is
relatively small, a coarse aggregation of cases
is needed for counts to be large enough to detect
hot-spots (monthly, by patrol beat).
City of Pittsburgh 55 sq. miles, divided into 6
precincts or 42 patrol car beats.
These limitations reduce the spatial and temporal
precision with which departments can pinpoint
crime clusters, as well as their ability to
respond rapidly to these clusters.
6
Expectation-based scan statistics
We aggregate weekly counts at a fine resolution
(1000 x 1000 ft. cells), and search for regions
(groups of cells) with higher than expected
counts.
Imagine moving a spatial window around the
surveillance area, allowing the size, shape, and
temporal duration to vary.
7
Expectation-based scan statistics
We aggregate weekly counts at a fine resolution
(1000 x 1000 ft. cells), and search for regions
(groups of cells) with higher than expected
counts.
Imagine moving a spatial window around the
surveillance area, allowing the size, shape, and
temporal duration to vary.
8
Expectation-based scan statistics
We aggregate weekly counts at a fine resolution
(1000 x 1000 ft. cells), and search for regions
(groups of cells) with higher than expected
counts.
Imagine moving a spatial window around the
surveillance area, allowing the size, shape, and
temporal duration to vary.
Is there any spatial window S and duration T such
that counts in S have been higher than expected
for the last T weeks?
We learn the expected counts from the historical
data by time series analysis.
9
Expectation-based scan statistics
2nd highest score 8.4
We find the highest-scoring space-time regions,
where the score of a region is computed by the
likelihood ratio statistic.
Not significant (p .098)
Maximum region score 9.8
Significant! (p .013)
Alternative hypothesis outbreak in region S
Null hypothesis no outbreak
These are the most likely clusters, and we can
compute the statistical significance of each
potential cluster by randomization testing.
10
The expectation-based model
qit is relative risk bit is expected count under
H0
Counts are Poisson distributed cit
Poisson(qitbit)
Under the null hypothesis H0, we expect counts to
be equal to baselines qit 1 everywhere.
Under the alternative hypothesis H1(S), we expect
increased risk in region S qit qin in S, for
some qin gt 1, and qit 1 outside.
qin 1.3
11
The expectation-based model
qit is relative risk bit is expected count under
H0
Counts are Poisson distributed cit
Poisson(qitbit)
Under the null hypothesis H0, we expect counts to
be equal to baselines qit 1 everywhere.
Under the alternative hypothesis H1(S), we expect
increased risk in region S qit qin in S, for
some qin gt 1, and qit 1 outside.
qin 1.3
This gives a simple and efficiently computable
likelihood ratio statistic
12
Pittsburgh crime data
We obtained crime offense report data for
1990-1999 from the Pittsburgh Bureau of Police
(date/time, street address, offense type).
We used ArcGIS to map street addresses to a 52 x
64 grid of 1000 x 1000 foot cells.
We considered two subsets of crime offenses
violent crimes such as murder and robbery, and
leading indicator crimes such as disorderly
conduct.
Total counts 25,838 VC / 200,032 LI
In previous work, Gorr et al. have shown that LI
crimes lead VC by 1 month.
13
Pittsburgh crime data
We obtained crime offense report data for
1990-1999 from the Pittsburgh Bureau of Police
(date/time, street address, offense type).
We used ArcGIS to map street addresses to a 52 x
64 grid of 1000 x 1000 foot cells.
We considered two subsets of crime offenses
violent crimes such as murder and robbery, and
leading indicator crimes such as disorderly
conduct.
Total counts 25,838 VC / 200,032 LI
In previous work, Gorr et al. have shown that LI
crimes lead VC by 1 month.
LI Oct 1996 VC Nov 1996
14
Results crime detection
For each of the two Pittsburgh crime datasets
(LI, VC), we used the expectation-based scan
statistic to predict the expected count of each
cell for each week, and to detect circular
space-time clusters (radius 20, duration 1-4
weeks) with higher than expected counts.
For the 477 weeks of violent crime data from
1991-1999, we found 93 clusters (81 primary 12
secondary clusters) that were significant at a
.01, a detection rate considered acceptable by
domain users.
How to tell whether the detected clusters are
useful? The challenge is that we do not have a
gold standard dataset (i.e. a
labeled set of crime hot-spots) to compare
against.
We use the detected clusters of violent crime as
a gold standard, and see how well we can
predict these clusters using the LI data.
15
Results crime prediction
How many of the 93 detected clusters of violent
crime could have been predicted by detecting
clusters of leading indicator crimes?
A VC cluster was counted as successfully
predicted if one of the 100 highest-scoring LI
clusters was spatially close to that cluster
(distance between centers 10) and 1-3 weeks
prior.
We used a randomization test to compare the
number of clusters successfully predicted by the
LI data to the number of successfully predicted
clusters that we would expect just by chance.
Result we successfully predicted 19 of the 93 VC
clusters (20), significantly more than the 10.7
expected by chance (p lt .02).
Considering only the 60 highest-scoring VC
clusters, we could predict 18 clusters (30),
nearly triple the 6.7 expected by chance (p lt
.003).
16
Results crime prediction
More generally, how well can we predict the top x
clusters of violent crime, using the top y
clusters of leading indicator crimes?
17
Discussion and future work
The next phase of our work will compare the
detected VC and LI clusters to a gold standard VC
dataset labeled by human experts. This will
allow us to better evaluate both our detection
accuracy and prediction accuracy, using the
detected VC and LI clusters respectively.
We are in the process of obtaining 911 call data
from computer-aided police dispatches, indexed by
location, date/time, and complaint type. Prior
work by Gorr et al. suggests that this dataset is
a strong leading indicator of violent crimes, and
thus will likely improve predictions.
Multivariate detection methods such as the
multivariate Bayesian scan statistic may allow us
to better integrate multiple streams of crime
data.
What data sources can be used for prediction in
the disease surveillance domain (animal disease
clusters, pollution levels, )
18
Conclusions
Analysis of the Pittsburgh crime data
demonstrates that scan statistics can efficiently
and accurately detect significant clusters of
crime, at a higher spatial and temporal
resolution than previously proposed methods.
By automatically detecting clusters of leading
indicator crimes, we can predict clusters of
violent crime between 1-3 weeks in advance.
By predicting where crime clusters will occur,
police departments can dynamically allocate
patrols to these areas and carry out other
interventions to prevent crime.
Thanks for listening! Any questions?