The Spatial Scale and Spread of Child Victimization

Previous research shows that large, densely populated urban areas have higher rates of child victimization that have persisted over time. However, few investigations have inquired about the processes that produce and sustain hot and cold spots of child victimization. As a result, the mechanisms that produce the observed spatial clustering of child victimization, and hence "why" harms against children tend to cluster in space, remains unknown. Does the likelihood of being a victim of violence in one location depend on a similar event happening in a nearby location within a specified timeframe? Rather, are child victims of violence more likely to reside in suboptimal neighborhood conditions? This paper aims to present an analytical and theoretical framework for distinguishing between these locational (point) processes to determine whether the empirical spatial patterns undergirding child victimization are more reflective of the "spread" via contagion (i.e., dependency) or whether they are produced by neighborhood structural inequality resulting from spatial heterogeneity. To detect spatial dependence, we applied the inhomogeneous K-function to Los Angeles Medical Examiner data on child homicide victim locations while controlling for regional differences in victimization events (i.e., heterogeneity). Our analysis found strong evidence of spatial clustering in child victimization at small spatial scales but inhibition at larger scales. We further found limited support for the spatiotemporal clustering of child victimization indicative of a contagion effect. Overall, our results support the role of neighborhood structural vulnerability in the underlying mechanisms producing patterns of child victimization across Los Angeles County. We conclude by discussing the policy implications for understanding this spatial patterning in geographical context and for developing effective and targeted preventive interventions.

Generalized functional linear model with a point process predictor

Point process data have become increasingly popular these days. For example, many of the data captured in electronic health records (EHR) are in the format of point process data. It is of great interest to study the association between a point process predictor and a scalar response using generalized functional linear regression models. Various generalized functional linear regression models have been developed under different settings in the past decades. However, existing methods can only deal with functional or longitudinal predictors, not point process predictors. In this article, we propose a novel generalized functional linear regression model for a point process predictor. Our proposed model is based on the joint modeling framework, where we adopt a log-Gaussian Cox process model for the point process predictor and a generalized linear regression model for the outcome. We also develop a new algorithm for fast model estimation based on the Gaussian variational approximation method. We conduct extensive simulation studies to evaluate the performance of our proposed method and compare it to competing methods. The performance of our proposed method is further demonstrated on an EHR dataset of patients admitted into the intensive care units of the Beth Israel Deaconess Medical Center between 2001 and 2008.

Modeling Event Propagation via Graph Biased Temporal Point Process

Temporal point process is widely used for sequential data modeling. In this article, we focus on the problem of modeling sequential event propagation in graph, such as retweeting by social network users and news transmitting between websites. Given a collection of event propagation sequences, the conventional point process model considers only the event history, i.e., embed event history into a vector, not the latent graph structure. We propose a graph biased temporal point process (GBTPP) leveraging the structural information from graph representation learning, where the direct influence between nodes and indirect influence from event history is modeled. Moreover, the learned node embedding vector is also integrated into the embedded event history as side information. Experiments on a synthetic data set and two real-world data sets show the efficacy of our model compared with conventional methods and state-of-the-art ones.

Self-exciting point process modelling of crimes on linear networks

Although there are recent developments for the analysis of first and second-order characteristics of point processes on networks, there are very few attempts in introducing models for network data. Motivated by the analysis of crime data in Bucaramanga (Colombia), we propose a spatiotemporal Hawkes point process model adapted to events living on linear networks. We first consider a non-parametric modelling strategy, for which we follow a non-parametric estimation of both the background and the triggering components. Then we consider a semi-parametric version, including a parametric estimation of the background based on covariates, and a non-parametric one of the triggering effects. Our model can be easily adapted to multi-type processes. Our network model outperforms a planar version, improving the fitting of the self-exciting point process model.

Impact of Driving Behavior on Commuter’s Comfort during Cab Rides: Towards a New Perspective of Driver Rating

Commuter comfort in cab rides affects driver rating as well as the reputation of ride-hailing firms like Uber/Lyft. Existing research has revealed that commuter comfort not only varies at a personalized level but also is perceived differently on different trips for the same commuter. Furthermore, there are several factors, including driving behavior and driving environment, affecting the perception of comfort. Automatically extracting the perceived comfort level of a commuter due to the impact of the driving behavior is crucial for a timely feedback to the drivers, which can help them to meet the commuter’s satisfaction. In light of this, we surveyed around 200 commuters who usually take such cab rides and obtained a set of features that impact comfort during cab rides. Following this, we develop a system Ridergo  which collects smartphone sensor data from a commuter, extracts the spatial time series feature from the data, and then computes the level of commuter comfort on a five-point scale with respect to the driving. Ridergo  uses a Hierarchical Temporal Memory model-based approach to observe anomalies in the feature distribution and then trains a Multi-task learning-based neural network model to obtain the comfort level of the commuter at a personalized level. The model also intelligently queries the commuter to add new data points to the available dataset and, in turn, improve itself over periodic training. Evaluation of Ridergo  on 30 participants shows that the system could provide efficient comfort score with high accuracy when the driving impacts the perceived comfort.

BAYESIAN MITIGATION OF SPATIAL COARSENING FOR A HAWKES MODEL APPLIED TO GUNFIRE, WILDFIRE AND VIRAL CONTAGION

Self-exciting spatiotemporal Hawkes processes have found increasing use in the study of large-scale public health threats, ranging from gun violence and earthquakes to wildfires and viral contagion. Whereas many such applications feature locational uncertainty, that is, the exact spatial positions of individual events are unknown, most Hawkes model analyses to date have ignored spatial coarsening present in the data. Three particular 21st century public health crises-urban gun violence, rural wildfires and global viral spread-present qualitatively and quantitatively varying uncertainty regimes that exhibit: (a) different collective magnitudes of spatial coarsening, (b) uniform and mixed magnitude coarsening, (c) differently shaped uncertainty regions and-less orthodox-(d) locational data distributed within the "wrong" effective space. We explicitly model such uncertainties in a Bayesian manner and jointly infer unknown locations together with all parameters of a reasonably flexible Hawkes model, obtaining results that are practically and statistically distinct from those obtained while ignoring spatial coarsening. This work also features two different secondary contributions: first, to facilitate Bayesian inference of locations and background rate parameters, we make a subtle yet crucial change to an established kernel-based rate model, and second, to facilitate the same Bayesian inference at scale, we develop a massively parallel implementation of the model's log-likelihood gradient with respect to locations and thus avoid its quadratic computational cost in the context of Hamiltonian Monte Carlo. Our examples involve thousands of observations and allow us to demonstrate practicality at moderate scales.

Ubiquitous Power Law Scaling in Nonlinear Self-Excited Hawkes Processes

The origin(s) of the ubiquity of probability distribution functions with power law tails is still a matter of fascination and investigation in many scientific fields from linguistic, social, economic, computer sciences to essentially all natural sciences. In parallel, self-excited dynamics is a prevalent characteristic of many systems, from the physics of shot noise and intermittent processes, to seismicity, financial and social systems. Motivated by activation processes of the Arrhenius form, we bring the two threads together by introducing a general class of nonlinear self-excited point processes with fast-accelerating intensities as a function of "tension." Solving the corresponding master equations, we find that a wide class of such nonlinear Hawkes processes have the probability distribution functions of their intensities described by a power law on the condition that (i) the intensity is a fast-accelerating function of tension, (ii) the distribution of marks is two sided with nonpositive mean, and (iii) it has fast-decaying tails. In particular, Zipf's scaling is obtained in the limit where the average mark is vanishing. This unearths a novel mechanism for power laws including Zipf's law, providing a new understanding of their ubiquity.

Asymmetric excitation of left- and right-tail extreme events probed using a Hawkes model: Application to financial returns

We construct a two-tailed peaks-over-threshold Hawkes model that captures asymmetric self- and cross-excitation in and between left- and right-tail extreme values within a time series. We demonstrate its applicability by investigating extreme gains and losses within the daily log-returns of the S&P 500 equity index. We find that the arrivals of extreme losses and gains are described by a common conditional intensity to which losses contribute twice as much as gains. However, the contribution of the former decays almost five times more quickly than that of the latter. We attribute these asymmetries to the different reactions of market traders to extreme upward and downward movements of asset prices: an example of negativity bias, wherein trauma is more salient than euphoria.

Interevent-time distribution and aftershock frequency in non-stationary induced seismicity

The initial footprint of an earthquake can be extended considerably by triggering of clustered aftershocks. Such earthquake-earthquake interactions have been studied extensively for data-rich, stationary natural seismicity. Induced seismicity, however, is intrinsically inhomogeneous in time and space and may have a limited catalog of events; this may hamper the distinction between human-induced background events and triggered aftershocks. Here we introduce a novel Gamma Accelerated-Failure-Time model for efficiently analyzing interevent-time distributions in such cases. It addresses the spatiotemporal variation and quantifies, per event, the probability of each event to have been triggered. Distentangling the obscuring aftershocks from the background events is a crucial step to better understand the causal relationship between operational parameters and non-stationary induced seismicity. Applied to the Groningen gas field in the North of the Netherlands, our model elucidates geological and operational drivers of seismicity and has been used to test for aftershock triggering. We find that the hazard rate in Groningen is indeed enhanced after each event and conclude that aftershock triggering cannot be ignored. In particular we find that the non-stationary interevent-time distribution is well described by our Gamma model. This model suggests that 27.0(± 8.5)% of the recorded events in the Groningen field can be attributed to triggering.

Estimation, diagnostics, and extensions of nonparametric Hawkes processes with kernel functions

The Hawkes self-exciting model has become one of the most popular point-process models in many research areas in the natural and social sciences because of its capacity for investigating the clustering effect and positive interactions among individual events/particles. This article discusses a general nonparametric framework for the estimation, extensions, and post-estimation diagnostics of Hawkes models, in which we use the kernel functions as the basic smoothing tool.