Browsing by Author "Short, Martin"

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    Reducing Bias in Estimates for the Law of Crime Concentration
    (Springer, 2019) Mohler, George; Brantingham, P. Jeffrey; Carter, Jeremy; Short, Martin; Computer and Information Science, School of Science
    Objectives The law of crime concentration states that half of the cumulative crime in a city will occur within approximately 4% of the city’s geography. The law is demonstrated by counting the number of incidents in each of N spatial areas (street segments or grid cells) and then computing a parameter based on the counts, such as a point estimate on the Lorenz curve or the Gini index. Here we show that estimators commonly used in the literature for these statistics are biased when the number of incidents is low (several thousand or less). Our objective is to significantly reduce bias in estimators for the law of crime concentration. Methods By modeling crime counts as a negative binomial, we show how to compute an improved estimate of the law of crime concentration at low event counts that significantly reduces bias. In particular, we use the Poisson–Gamma representation of the negative binomial and compute the concentration statistic via integrals for the Lorenz curve and Gini index of the inferred continuous Gamma distribution. Results We illustrate the Poisson–Gamma method with synthetic data along with homicide data from Chicago. We show that our estimator significantly reduces bias and is able to recover the true law of crime concentration with only several hundred events. Conclusions The Poisson–Gamma method has applications to measuring the concentration of rare events, comparisons of concentration across cities of different sizes, and improving time series estimates of crime concentration.
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    The Role of Graphlets in Viral Processes on Networks
    (Springer, 2018) Khorshidi, Samira; Al Hasan, Mohammad; Mohler, George; Short, Martin; Computer and Information Science, School of Science
    Predicting the evolution of viral processes on networks is an important problem with applications arising in biology, the social sciences, and the study of the Internet. In existing works, mean-field analysis based upon degree distribution is used for the prediction of viral spreading across networks of different types. However, it has been shown that degree distribution alone fails to predict the behavior of viruses on some real-world networks and recent attempts have been made to use assortativity to address this shortcoming. In this paper, we show that adding assortativity does not fully explain the variance in the spread of viruses for a number of real-world networks. We propose using the graphlet frequency distribution in combination with assortativity to explain variations in the evolution of viral processes across networks with identical degree distribution. Using a data-driven approach by coupling predictive modeling with viral process simulation on real-world networks, we show that simple regression models based on graphlet frequency distribution can explain over 95% of the variance in virality on networks with the same degree distribution but different network topologies. Our results not only highlight the importance of graphlets but also identify a small collection of graphlets which may have the highest influence over the viral processes on a network.