Prospective crime mapping in operational context Final report

A further point of note concerns the trade-off between having cells of small proportions, whichincreases the precision of the maps generated, and the time taken to complete thecalculations. For instance, the generation of a forecast for a grid which has 100m x 100mcells will take one-quarter of the time that it would take to complete the same task for a gridwhich contains cells that are 50m x 50m. Where analyses are required for an area the size of‘A’ Division, this can be of considerable importance. One issue then concerns the timelyproduction of the forecasts, a consideration whose importance will be amplified if the analysthas to produce forecasts within a limited window of time.The next issue concerns the bandwidth used. As is illustrated in Figure 2.2(4), Promap usestwo bandwidths. The first, the spatial bandwidth, may be calibrated in a variety of ways butshould relate to the distance over which the risk of victimisation is communicable.The second type of bandwidth concerns the time elapsed since a crime occurred and theproduction of the forecast. This bandwidth is conditional upon the first, as a burglary eventshould contribute to the risk intensity value of a cell only if it occurred within a given distanceof that cell. As with the spatial parameter, for the temporal bandwidth a variety of settingscould be used but again this should reflect the period of time over which the communicabilityof risk can reasonably be expected to endure, or slightly longer.A further methodological difference between the authors’ approach and that used inretrospective hotspotting lies in avoiding use of the distance from the midpoint of the cell andthe relevant burglary events in the derivation of the risk intensity values. Consider that forretrospective hotspotting a risk intensity value is calculated for the midpoint of the cell and thisvalue is then allocated to all other points within that cell. If risk intensity values werecomputed for all points within a cell it is unlikely that they would be identical. Thus, using thevalue for the centroid of the cell gives the impression that the risk of victimisation is uniformacross the cell. This is unlikely to be true. This problem will be amplified as the cell sizeincreases. Instead of using the exact Euclidian distance between all events and the cellmidpoint, for Promap the number of cells, the actual unit of analysis considered, between theevent and the cell is instead used. Thus, if a crime occurred within the cell underconsideration, the distance would be zero (actually, for computational reasons 1), if itoccurred within an adjacent cell, two, and so on. By adopting this approach the risk intensityvalues for each cell are likely to reflect more accurately the risks across the entire cell, ratherthan at one single point. Formula (2) was used to derive the risk intensity values for theprospective map, as follows:⎛ 1 ⎞ 1λτ( s)= ∑⎜1+ ∗ci ei c⎟(2)≤τ∩ ≤υ⎝ i ⎠ eiWhere,τ(s)bandwidthc i = number of cells between each point (i) within the bandwidth and the celle i = time elapsed for each point (i) within the temporal bandwidthλ = risk intensity value for cell s τ = spatial bandwidth υ = temporalEvaluating the accuracy of the different methodsAs discussed in earlier work (e.g. Bowers et al., 2004), there has been little attention given tothe measurement of the accuracy of mapping techniques used to inform the deployment ofoperational resources. This is clearly essential. For this reason, in earlier papers the authorsproposed a number of different standard metrics. These include the hit rate, which is simplythe number of future crimes correctly identified. A second important factor is the area of the‘at risk’ locations to be policed. Where operational resources are limited, to compare twotechniques one may need to equate the latter to allow a like-for-like comparison. One way ofcontrolling for this is to select the same geographic area for each method and then comparethe hit rate for each. Where possible this approach has been adopted in what follows. Arelated question concerns the area that should be selected within which crime could occur. In20