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Quantitative Criminology: Bayesian Statistics for Measuring the Dark Figure of Crime

Conference Paper

Quantitative Criminology: Bayesian Statistics for Measuring the Dark Figure of Crime

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Content may be subject to copyright.
1
A bit of background
Each countrys national crime statistics
determines rates of crime
Not all crimes counted, i.e. not recorded
by or reported to legal agencies or police
2
3
What is The Dark Figureof Crime?
The number of committed crimes that
are never reported or are never recorded
by legal or law enforcement agencies
So why is this?
4
1. Not all crimes are detected
5
Hidden
Too small
Not
crime
Not
noticed
Not
known
2. Not all crimes are reported
6
No evidence
Too trivial
Stigma
Humiliation or
embarrassment
No evidence
3. Not all crimes are recorded
Work load
Lost from records
No criming
Priorities
Other
7
3. Not all crimes are recorded-Contd
Fear of police
Fear of reporting a crime
8
3. Not all crimes are recorded-Contd
Feel embarrassed
Too trivial offence
9
3. Not all crimes are recorded-Contd
Police will not be able to do
anything about it
Not knowing a crime committed
10
Huge stigma
Other
11
So what can we do to get away from
this?
12
Aim to count crimes that have not recorded
by or reported to legal agencies or police for
whatever reason13
Police
records
Crime
surveys
Offending
surveys
Victim
surveys
Self-report
studies
Butall traditional crime measures
have a dark figure to some degree:
Respondent may not remember the
crime
Sampling errors
Respondent may not be honest
Respondent may be ashamed or
embarrassed
Respondent may exaggerate the nature
of crime, etc.14
15
The failure to report/record crimes
raises questions about the accuracy of
all crime statistics
16
The Current Situation
So many crimes take place in any given place
at a given period of time
There is a difference between committed
crimes and reported/recorded crimes, and this
MUST be calculated/identified
Our research is going to provide a solution to
this problem
Suggested Solution: Bayesian Probability
Posterior probability
Prior rational Belief New Evidence
Prior rational belief + New evidence = improved belief
This will allow to combine initial rates of crimes
determined by historical evidence with the rate
determined by the measurement.
17
What is the aim?
Account for crimes outside the boundaries of
all crime measures to:
Test theories of offending and victimization
Assess and develop crime stopping/fighting
polices
Provide mathematically based information
about the actual rates of crime
18
How it works in practice?
Determine the prior probability
Use random variables to determine (Posterior
probability) about an unrecorded/unreported
crime in question
Use BayesTheorem:


19
How to it works in practice? (Contd)
P (
A
)is the prior probability: either police
records, crime survey, offender survey, etc;or
a state of knowledge or degree of rational belief
P(B)is the secondary probability: either banks,
insurance companies, prison, private sector,
hospitals, other government agencies, etc;or
calculating probabilities
P (
B
/
A
)is the conditional probability of observing
variable
B
given that
A
is true or known.
P (
A
/
B
)is the conditional probability of observing
variable
A
given that
B
is true or known.
20
Confusing.?!
21
Example (1)
A crime statistics shows 100 recorded drug
offences, 80 drug trafficking offences and 20 drug
possession offences, but you know that there are 60
drug trafficking offences and 40 drug possession
offences. In the light of this new information, what is
your revised probability about the drug offences
rate?

 as P (trafficking model/trafficking data) = 0.75 x 0.8/1=
0.6=60% (drug trafficking rate)

 as P (possession model/possession data) = 2 x 0.2/1=
0.4=40% (drug possession rate) 22
Example (2)
If a night time burglary crime rate (25%) but you
believe its rate is higher (50%) and 90%of
burglary crimes occur at night then:
P(burglary/night)=    


  
= 45%
In this instance 45%is the actual rate of night
burglary.
23
How to interpret it?
If the measurement supports a prior
belief, the new test results will reinforce
it
If the measurement contradicts a prior
belief, the new test results will weaken it
and be taken seriously
If the measurement is relatively close to
a prior belief, the new results will confirm
it.24
Example (3)
Suppose we want to calculate the probability
of sexual abuse crime rate, but we know
nothing about it. From past data, suppose it is
10%. Next suppose we know that crime rate is
20% among the offenders aged 24 to 30.
P (1% rate sexual abuse/24-30 age group)
=  
 ?? = 2.5%. The rate of the sexual
abuse crime among the 24-30 year old age
group is equal to 25%, which is higher than
10%.
25
Scenarios can be much more complex than
these three examples calculated above! E.g.
a particular unrecorded/unreported crime
has three or four priors!
26
Example (4):
A rate of sexual abuse crimes:
-victim survey record: there is a 50% decrease,
with the numbers of crimes 150
-police record: there is a 60% decrease, with the
numbers of crimes 50
-offender survey record: there is a 30% decrease,
with the numbers of crimes 100
Victim survey record showed a 50 % decrease in
the rate a sexual abuse crime, what is the
probability that this rate is correct? 27
P (victim survey/rate) = P (victim survey) P
(rate/victim survey) / P (victim survey) P
(rate/victim survey) + P (police) p (rate/police) + P
(offender survey) P (rate/offender survey)
Add up the number of crimes: 150 + 50 +100 =
300
P (victim survey/rate) = (150/300) x 50% /
(150/300) x 50% + (50/300) x 60% + (100/300) x
30%
P (victim survey/rate) = 150 x 50% / 150 x 50 % +
50 x60% + 100 x 30 = 0.25 / 0.25 + 0.096+ 0.099=
0.25/ 0.445= 0.56%. The result remains close to
the prior belief from the victim survey. 28
Advantages
Past or Prior
information is
widely available
If a prior information
is encouraging, less
new inquiry may be
needed to confirm
the estimate of a
particular crime rate
Disadvantages
Past or prior
information may not
be accurate
Some may not accept
validity of past or
prior information
There is no agreed
way to select a prior
29
Questions!
30
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