Related papers: A non-parametric Hawkes process model of primary a…
Secondary crash likelihood prediction is a critical component of an active traffic management system to mitigate congestion and adverse impacts caused by secondary crashes. However, existing approaches mainly rely on post-crash features…
Analysis of heterogeneous patterns in complex spatio-temporal data finds usage across various domains in applied science and engineering, including training autonomous vehicles to navigate in complex traffic scenarios. Motivated by…
The self-exciting Hawkes process is widely used to model events which occur in bursts. However, many real world data sets contain missing events and/or noisily observed event times, which we refer to as data distortion. The presence of such…
This paper demonstrates the applicability of the safe model predictive control (SMPC) framework to autonomous driving scenarios, focusing on the design of adaptive cruise control (ACC) and automated lane-change systems. Building on the SMPC…
Across a wide variety of applications, the self-exciting Hawkes process has been used to model phenomena in which the history of events influences future occurrences. However, there may be many situations in which the past events only…
Hawkes processes are a class of self-exciting point processes that are used to model complex phenomena. While most applications of Hawkes processes assume that event data occurs in continuous-time, the less-studied discrete-time version of…
Hawkes processes are a particularly interesting class of stochastic process that have been applied in diverse areas, from earthquake modelling to financial analysis. They are point processes whose defining characteristic is that they…
Aggressive behavior in autistic inpatient youth often arises in temporally clustered bursts complicating efforts to distinguish external triggers from internal escalation. The sample population branching factor-the expected number of new…
Traditionally, Hawkes processes are used to model time--continuous point processes with history dependence. Here we propose an extended model where the self--effects are of both excitatory and inhibitory type and follow a Gaussian Process.…
Predicting discrete events in time and space has many scientific applications, such as predicting hazardous earthquakes and outbreaks of infectious diseases. History-dependent spatio-temporal Hawkes processes are often used to…
Patient healthcare utilization consists of irregularly time-stamped events, such as outpatient visits, inpatient admissions, and emergency encounters, forming individualized care trajectories. Modeling these trajectories is crucial for…
The Hawkes process is a simple point process that has long memory, clustering effect, self-exciting property and is in general non-Markovian. The future evolution of a self-exciting point process is influenced by the timing of the past…
Crimes emerge out of complex interactions of human behaviors and situations. Linkages between crime incidents are highly complex. Detecting crime linkage given a set of incidents is a highly challenging task since we only have limited…
We propose a simulation method for multidimensional Hawkes processes based on superposition theory of point processes. This formulation allows us to design efficient simulations for Hawkes processes with differing exponentially decaying…
The marked Hawkes risk process is a compound point process for which the occurrence and amplitude of past events impact the future. Thanks to its autoregressive properties, it found applications in various fields such as neuosciences,…
We adopt the interpretability offered by a parametric, Hawkes-process-inspired conditional probability mass function for the marks and apply variational inference techniques to derive a general and scalable inferential framework for marked…
Locally stationary Hawkes processes have been introduced in order to generalise classical Hawkes processes away from stationarity by allowing for a time-varying second-order structure. This class of self-exciting point processes has…
In this paper, we introduce a non-parametric memory representation for spatio-temporal segmentation that captures the local space and time around an autonomous vehicle (AV). Our representation has three important properties: (i) it…
Analysis of gun violence in the United States has utilized various models based on spatiotemporal point processes. Previous studies have identified a contagion effect in gun violence, characterized by bursts of diffusion across urban…
Road traffic accidents remain a major public health challenge worldwide, with urbanisation and population density identified as key factors influencing risk. This study analyses monthly accident data from 2009 to 2023 across 632…