George Mohler

Self-Exciting Point Process Modeling of Crime

Highly clustered event sequences are observed in certain types of crime data, such as burglary and gang violence, due to crime-specific patterns of criminal behavior. Similar clustering patterns are observed by seismologists, as earthquakes are well known to increase the risk of subsequent earthquakes, or aftershocks, near the location of an initial event. Space–time clustering is modeled in seismology by self-exciting point processes and the focus of this article is to show that these methods are well suited for criminological applications. We first review self-exciting point processes in the context of seismology. Next, using residential burglary data provided by the Los Angeles Police Department, we illustrate the implementation of self-exciting point process models in the context of urban crime. For this purpose we use a fully nonparametric estimation methodology to gain insight into the form of the space–time triggering function and temporal trends in the background rate of burglary.

Improving density estimation by incorporating spatial information

Given discrete event data, we wish to produce a probability density that can model the relative probability of events occurring in a spatial region. Common methods of density estimation, such as Kernel Density Estimation, do not incorporate geographical information. Using these methods could result in nonnegligible portions of the support of the density in unrealistic geographic locations. For example, crime density estimation models that do not take geographic information into account may predict events in unlikely places such as oceans, mountains, and so forth. We propose a set of Maximum Penalized Likelihood Estimation methods based on Total Variation and Sobolev norm regularizers in conjunction with a priori high resolution spatial data to obtain more geographically accurate density estimates. We apply this method to a residential burglary data set of the San Fernando Valley using geographic features obtained from satellite images of the region and housing density information.

Fast TV Regularization for 2D Maximum Penalized Likelihood Estimation

Total Variation-based regularization, well established for image processing applications such as denoising, was recently introduced for Maximum Penalized Likelihood Estimation (MPLE) as an effective way to estimate nonsmooth probability densities. While the estimates show promise for a variety of applications, the nonlinearity of the regularization leads to computational challenges, especially in multidimensions. In this article we present a numerical methodology, based upon the Split Bregman L1 minimization technique, that overcomes these challenges, allowing for the fast and accurate computation of 2D TV-based MPLE. We test the methodology with several examples, including V-fold cross-validation with large 2D datasets, and highlight the application of TV-based MPLE to point process crime modeling. The proposed algorithm is implemented as the Matlab function TVMPLE. The Matlab (mex) code and datasets for examples and simulations are available as online supplements.

Non-local crime density estimation incorporating housing information

Given a discrete sample of event locations, we wish to produce a probability density that models the relative probability of events occurring in a spatial domain. Standard density estimation techniques do not incorporate priors informed by spatial data. Such methods can result in assigning significant positive probability to locations where events cannot realistically occur. In particular, when modelling residential burglaries, standard density estimation can predict residential burglaries occurring where there are no residences. Incorporating the spatial data can inform the valid region for the density. When modelling very few events, additional priors can help to correctly fill in the gaps. Learning and enforcing correlation between spatial data and event data can yield better estimates from fewer events. We propose a non-local version of maximum penalized likelihood estimation based on the H1 Sobolev seminorm regularizer that computes non-local weights from spatial data to obtain more spatially accurate density estimates. We evaluate this method in application to a residential burglary dataset from San Fernando Valley with the non-local weights informed by housing data or a satellite image.

Eliminating Malaria in the American South: An Analysis of the Decline of Malaria in 1930s Alabama

Until the 1930s, malaria was endemic throughout large swaths of the American South. We used a Poisson mixture model to analyze the decline of malaria at the county level in Alabama (an archetypical Deep South cotton state) during the 1930s. Employing a novel data set, we argue that, contrary to a leading theory, the decline of malaria in the American South was not caused by population movement away from malarial areas or the decline of Southern tenant farming. We elaborate and provide evidence for an alternate explanation that emphasizes the role of targeted New Deal-era public health interventions and the development of local-level public health infrastructure. We show that, rather than disappearing as a consequence of social change or economic improvements, malaria was eliminated in the Southern United States in the face of economic dislocation and widespread and deep-seated poverty.

Does Predictive Policing Lead to Biased Arrests? Results From a Randomized Controlled Trial

ABSTRACT Racial bias in predictive policing algorithms has been the focus of a number of recent news articles, statements of concern by several national organizations (e.g., the ACLU and NAACP), and simulation-based research. There is reasonable concern that predictive algorithms encourage directed police patrols to target minority communities with discriminatory consequences for minority individuals. However, to date there have been no empirical studies on the bias of predictive algorithms used for police patrol. Here, we test for such biases using arrest data from the Los Angeles predictive policing experiments. We find that there were no significant differences in the proportion of arrests by racial-ethnic group between control and treatment conditions. We find that the total numbers of arrests at the division level declined or remained unchanged during predictive policing deployments. Arrests were numerically higher at the algorithmically predicted locations. When adjusted for the higher overall crime rate at algorithmically predicted locations, however, arrests were lower or unchanged.

Spatial Concentration of Opioid Overdose Deaths in Indianapolis: An Application of the Law of Crime Concentration at Place to a Public Health Epidemic

The law of crime concentration at place has become a criminological axiom and the foundation for one of the strongest evidence-based policing strategies to date. Using longitudinal data from three sources, emergency medical service calls, death toxicology reports from the Marion County (Indiana) Coroner’s Office, and police crime data, we provide four unique contributions to this literature. First, this study provides the first spatial concentration estimation of opioid-related deaths. Second, our findings support the spatial concentration of opioid deaths and the feasibility of this approach for public health incidents often outside the purview of traditional policing. Third, we find that opioid overdose death hot spots spatially overlap with areas of concentrated violence. Finally, we apply a recent method, corrected Gini coefficient, to best specify low-N incident concentrations and propose a novel method for improving upon a shortcoming of this approach. Implications for research and interventions are discussed.