1. Measuring Repeat and Near-Repeat Burglary Effects
Martin B. Short, Maria R. D’Orsogna,
P. Jeffrey Brantingham, George E. Tita
Maria Pavlovskaia

2. Repeat and Near-Repeat Victimization
Criminals likely to revisit crime scene
Likely to rob neighbors of previous victims
- Recently, the idea of repeat and near repeat victimization has emerged as an important focus in criminology.
- In the case of repeat victimization, this is the hypothesis that a victim, and for this paper, specifically the victim of a burglary, is likely to be robbed again within a short period of time. This is because criminals often prefer to revisit houses that they have previously robbed.
- Near-repeat victimization is a similar idea, stating that the neighbors of a previously robbed house are at an increased risk because the criminal is likely to return to the vicinity of a previously robbed house.

3. Why? Knowledge of entry modes and security Easy access to site
Abundance of material possessions
Knowledge of neighbor’s daily routines
- Now, you might ask, why would a criminal return to a house that he has already robbed? At first this may seem counterintuitive because the criminal appears at an increased risk from the already frightened residents.
- However, there are many benefits to returning to a pervious target.
- The criminal already knows how to get into the house and avoid security measures - He has easy access to the site - He may have been made aware of some valuable possessions in the house
- And he has already learned the neighbor’s daily routines in the process of canvassing the house

4. Data analysis
Measured the distribution of wait times between successive burglaries
Rapidly decaying function
Conclusion: houses likely to be robbed again within a short period of time of a burglary
Thus repeat victimization hypothesis is true?
- The repeat and near-repeat hypotheses have been repeatedly tested against real crime data and shown to be accurate. However, this paper takes a closer look at that data analysis and questions whether it really supports the idea of repeat and near-repeat victimization. - This is what was done in previous studies. - Anthropologists, or others, measured the distributions of wait times between successive burglaries
- They noted that the distribution is a rapidly decaying function. That is, many more short wait times were observed than long wait times.
- The conclusion that was made from this is that houses are more likely to be robbed again within a short period of time after a burglary and therefore the repeat victimization hypothesis holds true for the data. - However, does this really follow from the observation of the rapidly decaying function?

5. Random Event Hypothesis
Burglaries occur at random with rate 
Poisson process
Wait times exponentially distributed
- In the paper, the authors look at what would happen if the burglaries weren’t correlated in any way and happened completely at random.
- In this model, burglaries can happen at random with rate lambda. - This is known as a Poisson process - The probability density function of wait times between successive events in a Poisson process is the exponential distribution (in the continuous form, it’s the geometric distribution in the discrete form).
- You’ll notice that this is a rapidly decaying function although the modeled burglaries are uncorrelated and there is no repeat victimization effect. This is already suspicious because it means that when, before, they saw the rapidly decaying function and concluded that the repeat victimization effect was indeed present, they may have been looking at completely uncorrelated data.

6. Testing the REH Two different counting methods Sliding window method
Monitors each house for max days after burglary
Count the number of burglaries occur in that time
Fixed window method
Classify houses by number of times robbed
Look at the distribution of wait times in each class
- So now the question becomes, are the burglaries really uncorrelated and happening at random? The authors test the REH, or random event hypothesis against real crime data.
- etc.

7. Sliding Window Method Sample contains D days of data
Data split into N blocks with crime rates i
Corresponding weights wi
Predicted distribution:

8. Sliding Window Method Long Beach Data Set 3
- Here’s the results of the sliding window count. The histogram bars show the number of observed wait times between robberies. The white line is the best fit line of the form that our predicted distribution for random burglaries takes (the houses are broken up into only three groups).
- You can see that it fits very well, suggesting perhaps that the burglaries were indeed random.
- However, that’s not at all the conclusion we want, so we try the other counting method.

9. Fixed Window Method Sample contains D days of data
Only focus on houses robbed twice
Predicted distribution:
- The second counting method is the fixed window method. We’ve got D days of data, and we’ll only look at houses that were robbed twice over those D days. This is the predicted distribution. Let’s think about it for a second, because it’s actually pretty simple to understand. Let’s say D is 100 days. The only way that the robberies can be 99 days apart is if one happens on the first day, and the other happens on the last day. There’s not a huge likelihood of that. However, there are many ways that they can be one day apart. The first can happen on any one of 99 days, and the second one has to happen the day after. So for a time interval tau, there are D-tau ways that the robberies can be tau days apart. That is the D-tau factor that you see here. However, since this is a probability density function, it has to integrate to one, or since it’s discrete, it has to add up to one. To do this, we scale it by the total number of possible combinations over all the values of tau. This is the sum of D-tau for tau ranging from 1 to D-1, and that is (D)(D+1)/2. So it’s scaled by that, and this gives us our pdf. It’s nice because there are no variables here.

10. Fixed Window Method Long Beach Data Set
- Here we compare it with the data. You can see that the predicted distribution doesn’t fit the data at all.

11. REH disproved Robberies are correlated as hypothesized
Data supports the exact-repeat hypothesis
Burglarized houses likely to be struck again
Data also supports near-repeat hypothesis