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Graph neural networks (GNNs) provide a powerful and scalable solution for modeling continuous spatial data. However, they often rely on Euclidean distances to construct the input graphs. This assumption can be improbable in many real-world…
This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…
Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are {\em exactly} invariant under Euclidean scaling? This requires working in the continuum…
Real-time traffic prediction from high-fidelity spatiotemporal traffic sensor datasets is an important problem for intelligent transportation systems and sustainability. However, it is challenging due to the complex topological dependencies…
This paper describes continuous-space methodologies to estimate the collision probability, Euclidean distance and gradient between an ellipsoidal robot model and an environment surface modeled as a set of Gaussian distributions.…
Graph-based spatio-temporal neural networks are effective to model the spatial dependency among discrete points sampled irregularly from unstructured grids, thanks to the great expressiveness of graph neural networks. However, these models…
This paper leverages macroscopic models and multi-source spatiotemporal data collected from automatic traffic counters and probe vehicles to accurately estimate traffic flow and travel time in links where these measurements are unavailable.…
Recognizing traversable terrain from 3D point cloud data is critical, as it directly impacts the performance of autonomous navigation in off-road environments. However, existing segmentation algorithms often struggle with challenges related…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
In public health applications, spatial data collected are often recorded at different spatial scales and over different correlated variables. Spatial change of support is a key inferential problem in these applications and have become…
Traffic state prediction in a transportation network is paramount for effective traffic operations and management, as well as informed user and system-level decision-making. However, long-term traffic prediction (beyond 30 minutes into the…
Road traffic forecasting is crucial in real-world intelligent transportation scenarios like traffic dispatching and path planning in city management and personal traveling. Spatio-temporal graph neural networks (STGNNs) stand out as the…
Spatial statistics is concerned with the analysis of data that have spatial locations associated with them, and those locations are used to model statistical dependence between the data. The spatial data are treated as a single realisation…
For a long time, many methods are developed to make temporal signal analyses based on time series. However, for geographical systems, spatial signal analyses are as important as temporal signal analyses. Nonstationary spatial and temporal…
Accurate spatial prediction and rigorous uncertainty quantification are central to modern spatial epidemiology and environmental risk analysis. We introduce a statistically principled hybrid modelling framework that integrates the…
The R software package rSPDE contains methods for approximating Gaussian random fields based on fractional-order stochastic partial differential equations (SPDEs). A common example of such fields are Whittle-Mat\'ern fields on bounded…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
The identification of accident hot spots is a central task of road safety management. Bayesian count data models have emerged as the workhorse method for producing probabilistic rankings of hazardous sites in road networks. Typically, these…
Estimation of stationary dependence structure parameters using only a single realisation of the spatial process, typically leads to inaccurate estimates and poorly identified parameters. A common way to handle this is to fix some of the…
Efficient and accurate incident prediction in spatio-temporal systems is critical to minimize service downtime and optimize performance. This work aims to utilize historic data to predict and diagnose incidents using spatio-temporal…