Probability Model

    In the sci-fi movie Minority Report, the action takes place in 2054 in the crime prevention department. Employees of the department receive information from three "visionaries" whose visions are displayed on the screen. Future criminals are arrested even before he thought about implementing his plans.

    Today, this fantastic storyline is partially embodied in reality, with one important difference: instead of the "visionaries", information for police patrols is supplied by a mathematical model that calculates crime statistics in different areas of the city. The NY Times newspaper describes the work of police patrols in the city of Santa Cruz (California), where a similar crime prevention program operates in an experimental mode.

    Santa Cruz started testingthe program in July 2011 on an array of data on crimes against property (car thefts and thefts, house robberies). It is assumed that criminals tend to act in the usual areas of the city and at about the same time that they had successfully robbed.


    This graph displays gangster showdown statistics in a Los Angeles area and serves to demonstrate that certain types of crimes tend to be grouped by time and place.

    Based on crime statistics over the past few years, the lambda function λ (t) has been calculated . This graph shows how crime statistics are converted to frequency.



    The program calculates a similar parameter (crime rate) for each district of the city and type of crime. If you make a heat map, you get something like the following.



    The mathematical model is explained in more detail on the website of the University of Santa Clara, since the leading developer of the system is an employee of the university . In short, the model resembles the calculation of the probability of aftershocks- repeated seismic shocks, lower intensity compared to the main shock. As in the case of earthquakes, each crime also gives rise to waves of aftershocks, that is, increase the likelihood of new crimes in the same place in the future. Although one process takes place in the earth’s crust and the other in human society, oddly enough, similar formulas are used to describe them.

    One way or another, but practically nothing has changed in the work of the Santa Cruz patrol officers, they do their job exactly the same as before. Only every day they receive a new route for patrolling, indicating 10 "hot spots" of the route. Here's what this information looks like in the Google Maps interface.



    For each square measuring 150 by 150 meters, the probability of committing a crime in a 24-hour period (P), the distribution of this probability by two types of crime: automobile (Pveh) and home (Pres), the start time of the two most dangerous hour intervals (TW) are indicated.



    New data is added to the system every day. The photo shows the 911 call center dispatcher, who maps crime coordinates in real time.



    According to the head of the Santa Cruz police department, in the first month of testing, the system prevented several crimes and led to five arrests. The number of arrests, of course, is much less than the number of crimes prevented, because it is not always possible to prove malicious intent, but a potential attacker can be punished for another type of crime (for example, carrying firearms or possession of drugs). For an effective law enforcement system, crime prevention is more important than catching a criminal. So, in July 2011, the number of car robberies decreased by 27% compared with the same month of 2010.

    Improving the efficiency of patrols, the program also saves taxpayers' money, because due to the economic crisis, Santa Cruz police now have 20% fewer employees than in 2000. Now in a city with a population of 60,000 people, only 94 police officers remain, including 60 patrol officers.

    By the way, crime prediction departments are also being created in other cities in the USA, although they do not give direct instructions to patrol cars there. For example, last year a crime prediction department was set up at the Chicago police.

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