A spatio-temporal kernel density estimation framework for predictive crime hotspot mapping and evaluation

Abstract

Predictive hotspot mapping plays a critical role in hotspot policing. Existing methods such as the popular kernel density estimation (KDE) do not consider the temporal dimension of crime. Building upon recent works in related fields, this article proposes a spatio-temporal framework for predictive hotspot mapping and evaluation. Comparing to existing work in this scope, the proposed framework has four major features: (1) a spatio-temporal kernel density estimation (STKDE) method is applied to include the temporal component in predictive hotspot mapping, (2) a data-driven optimization technique, the likelihood cross-validation, is used to select the most appropriate bandwidths, (3) a statistical significance test is designed to filter out false positives in the density estimates, and (4) a new metric, the predictive accuracy index (PAI) curve, is proposed to evaluate predictive hotspots at multiple areal scales. The framework is illustrated in a case study of residential burglaries in Baton Rouge, Louisiana in 2011, and the results validate its utility.

Understanding the spatial distribution of crime in hot crime areas

“…Such a characteristic poses a challenge for hot area identification. In order to identify accurately the location of hot areas to benefit policing efficacy in deterring crime, numerous studies have been conducted in optimizing KDE (Maciejewski et al, 2010;Nakaya & Yano, 2010;Hu et al, 2018). Initially, KDE was implemented in the identification of spatial hot areas (Chainey & Ratcliffe, 2005;Eck et al, 2005).…”

“…Nakaya & Yano (2010) adopted the widely used Epanecknikov kernel in spatial temporal kernel estimation. Based on these two bodies of studies, a more recent study proposed a comprehensive method integrating time dimension and univariate kernel function to account for hotspot identification and crime prediction (Hu et al, 2018).…”

“…We introduced two spatial temporal kernel density estimation (STKDE) methods in our current research (Nakaya & Yano, 2010;Hu et al, 2018). The first method (STKDE1) (Nakaya & Yano et al, 2010) was used for the identification and display of hot areas.…”

“…The first method (STKDE1) (Nakaya & Yano et al, 2010) was used for the identification and display of hot areas. The second method (STKDE2) (Hu et al, 2018) was used for hot area identification and crime prediction.…”

“…Bandwidth selection is a critical step in kernel density estimation due to its crucial impact on risk surface (Hu et al, 2014). The cross-validation method is adopted for the bandwidth selection in the STKDE2 method (Hu et al, 2018). A derived equation with a maximum value of log likelihood L determines the optimal bandwidths h x , h y and h t :…”