Michael D. Porter

Detecting local regions of change in high-dimensional criminal or terrorist point processes

A method is presented for detecting changes to the distribution of a criminal or terrorist point process between two time periods using a non-model-based approach. By treating the criminal/terrorist point process as an intelligent site selection problem, changes to the process can signify changes in the behavior or activity level of the criminals/terrorists. The locations of past events and an associated vector of geographic, environmental, and socio-economic feature values are employed in the analysis. By modeling the locations of events in each time period as a marked point process, we can then detect differences in the intensity of each component process. A modified PRIM (patient rule induction method) is implemented to partition the high-dimensional feature space, which can include mixed variables, into the most likely change regions. Monte Carlo simulations are easily and quickly generated under random relabeling to test a scan statistic for significance. By detecting local regions of change, not only can it be determined if change has occurred in the study area, but the specific spatial regions where change occurs is also identified. An example is provided of breaking and entering crimes over two-time periods to demonstrate the use of this technique for detecting local regions of change. This methodology also applies to detecting regions of differences between two types of events such as in case-control data.

GPU accelerated MCMC for modeling terrorist activity

The use of graphical processing unit (GPU) parallel processing is becoming a part of mainstream statistical practice. The reliance of Bayesian statistics on Markov Chain Monte Carlo (MCMC) methods makes the applicability of parallel processing not immediately obvious. It is illustrated that there are substantial gains in improved computational time for MCMC and other methods of evaluation by computing the likelihood using GPU parallel processing. Examples use data from the Global Terrorism Database to model terrorist activity in Colombia from 2000 through 2010 and a likelihood based on the explicit convolution of two negative-binomial processes. Results show decreases in computational time by a factor of over 200. Factors influencing these improvements and guidelines for programming parallel implementations of the likelihood are discussed.

Evaluating temporally weighted kernel density methods for predicting the next event location in a series

One aspect of tactical crime or terrorism analysis is predicting the location of the next event in a series. The objective of this article is to present a methodology to identify the optimal parameters and to test the performance of temporally weighted kernel density estimation models for predicting the next event in a criminal or terrorist event series. By placing event series in a space–time point pattern framework, the next event prediction models are shown to be based on estimating a conditional spatial density function. We use temporal weights that indicate how much influence past events have toward predicting future event locations, which can also incorporate uncertainty in the event timing. Results of applying this methodology to crime series in Baltimore County, MD, indicate that performance can vary greatly by crime type and little by series length and is fairly robust to choice of bandwidth.

Network neighborhood analysis

We present a technique to represent the structure of large social networks through ego-centered network neighborhoods. This provides a local view of the network, focusing on the vertices and their kth order neighborhoods allowing discovery of interesting patterns and features of the network that would be hidden in a global network analysis. We present several examples from a corporate phone call network revealing the ability of our methods to discover interesting network behavior that is only available at the local level. In addition, we present an approach to use these concepts to identify abrupt or subtle anomalies in dynamic networks.