Fig 1.
The dark figure of crime estimation.
Daily gathering crime observations obtain a daily update for the crime estimation (filled-in colors of small squares). Information coming from police visits (blue border squares), which decision planners can control, updates these estimations. Simultaneously, the information provided by crime events reported by citizens (green border squares) is also integrated. The decision planner may account for exploration-exploitation strategies by dynamically locating police visits.
Fig 2.
Bogotá, capital city of Colombia.
Figure shows the 19 jurisdictions in which the city is divided and our grid of 1 km2 cells. This figure was created by the authors using a shapefile of the administrative division of Bogotá, which is publicly available on the government’s “Datos abiertos” (Open data in Spanish) web page at https://datosabiertos.bogota.gov.co/dataset/localidad-bogota-d-c.
Fig 3.
Crimes by source of information: SIEDCO is the official source of information of crimes in Bogotá.
NUSE is the security and emergency call center of the city. Total is the sum of both sources eliminating double counting as explained in the main body of the text.
Table 1.
Results of Bogotá’s City Chamber of Commerce, Cámara de Comercio de Bogotá, victimization and reporting survey 2014.
We use reported rates form each jurisdiction to estimate underreporting simulated from our Poisson model. The table also reports the population of each jurisdiction and victimization rate.
Fig 4.
Panel (a), CUCB Convergence to true arms mean. Panel (b), CUCB Convergence to true arms underreporting parameters.
Table 2.
M is the number of arms, m the size of the super arm, Tmax the maximum number rounds played and n is the parameter of the Binomial distribution.
Table 3.
True values of μ and q for each arm in simulations.
Fig 5.
Algorithms convergence error and number of visits.
Panel (a), convergence error of true arms mean for each algorithm. The error is measured as the Euclidean distance between the true mean vector and the estimated mean vector per round. Panel (b), number of visits (i.e., fired arms) of algorithms to each arm.
Fig 6.
Convergence error of true arms mean for each algorithm.
The error is measured as the Euclidean distance between the true mean vector and estimated mean vector per round.
Table 4.
Time to completion of 1, 000 rounds of each of the three algorithms.
Case 1: M = 1, 000 and K = 100. Case 2: M = 10, 000 and K = 1, 000. Case 3: M = 50, 000 and K = 5, 000. Sec is seconds, min is minutes.
Fig 7.
Panel (a), convergence of the vector of incidence rates μ to the mean of all crimes per cell across time. The error is measured as the Euclidean distance between vectors with 415 components. Panel (b), convergence of estimated vector q per round to the empirical mean of the underreporting rate for the whole sample. The error is measured as the Euclidean distance between vectors with 415 components.
Fig 8.
Histogram of convergence of estimated error of q in the last round to the empirical mean of the underreporting rate for the whole sample.
Absolute values reported.
Fig 9.
Panel (a), convergence of the estimated total number of crimes to the observed number of crimes in the city. Panel (b), convergence of the estimated total (aggregate across cells) of the number of underreported crimes implied by the model.
Fig 10.
Heat map illustrating the convergence, using the CUCB algorithm, of the estimated crime and underreporting of events in the city, to the real values.
The first column, second and third rows show the heat maps of the estimated crime incidence rates after 25 and 100 iterations, respectively. The second column, first row shows real underreporting as measured by NUSE dataset. The second column, second and third rows show the heat maps of the estimated underreporting crime after 25 iterations and 100 iterations, respectively. This figure was created by the authors using a shapefile of the administrative division of Bogotá, which is publicly available on the government’s “Datos abiertos” (Open data in Spanish) web page at https://datosabiertos.bogota.gov.co/dataset/localidad-bogota-d-c.
Fig 11.
Panel (a), results for second application simulating data with standard crime Poisson model. Panel shows the convergence of the vector true incidence rates μ to the true values. Error measured as Euclidean distance between vectors. Panel (b), results for second application simulating data with a standard crime Poisson model. Figure shows the convergence of the vector parameters q to the true values. Error measured as the Euclidean distance between vectors. UCB1 not reported because it is outperformed by the other two algorithms.