This paper presents a standard mathematical notation for hot-spot indices and explores the mathematical intuition and knapsack problem inherent in evaluating the most recent index, the Prediction Efficiency Index (PEI), the authors conclude with future directions of the evaluation of hot-spot maps.
Hot-spot maps are used by a majority of police departments throughout the United States. These maps are used to determine policing decisions such as community resource allocation and police presence. There are various methods to generate these maps; however, there is no consensus on when each specific mapping technique is best to use. We argue this is due to a lack of understanding of how "good" a hot-spot map is relative to another. Many data scientists use statistical metrics to evaluate hot-spot maps, while many police departments and hot-spot software use indices developed in the criminology literature. This paper bridges the gap between these fields by advancing the mathematical understanding of recent criminology hot-spot indices. (Publisher abstract provided)
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