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Whittle-Mat\'ern fields are a recently introduced class of Gaussian processes on metric graphs, which are specified as solutions to a fractional-order stochastic differential equation. Unlike earlier covariance-based approaches for…
The modeling of spatial point processes has advanced considerably, yet extending these models to non-Euclidean domains, such as road networks, remains a challenging problem. We propose a novel framework for log-Gaussian Cox processes on…
The increasing availability of network data has driven the development of advanced statistical models specifically designed for metric graphs, where Gaussian processes play a pivotal role. While models such as Whittle-Mat\'ern fields have…
Intrinsic Gaussian fields are used in many areas of statistics as models for spatial or spatio-temporal dependence, or as priors for latent variables. However, there are two major gaps in the literature: first, the number and flexibility of…
We define a new class of Gaussian processes on compact metric graphs such as street or river networks. The proposed models, the Whittle--Mat\'ern fields, are defined via a fractional stochastic differential equation on the compact metric…
Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…
The classical tools in spatial statistics are stationary models, like the Mat\'ern field. However, in some applications there are boundaries, holes, or physical barriers in the study area, e.g. a coastline, and stationary models will…
We consider the problem of model selection in Gaussian Markov fields in the sample deficient scenario. In many practically important cases, the underlying networks are embedded into Euclidean spaces. Using the natural geometric structure,…
This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the…
Road casualties represent an alarming concern for modern societies. During the last years, several authors proposed sophisticated approaches to help authorities implement new policies. These models were usually developed considering a set…
This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…
The article studies non-Gaussian extensions of a recently discovered link between certain Gaussian random fields, expressed as solutions to stochastic partial differential equations (SPDEs), and Gaussian Markov random fields. The focus is…
To capture spatial relationships and temporal dynamics in traffic data, spatio-temporal models for traffic forecasting have drawn significant attention in recent years. Most of the recent works employed graph neural networks(GNN) with…
Metric graphs are useful tools for describing spatial domains like road and river networks, where spatial dependence act along the network. We take advantage of recent developments for such Gaussian Random Fields (GRFs), and consider joint…
The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but…
We present an approach to estimate the severity of traffic related accidents in aggregated (area-level) and disaggregated (point level) data. Exploring spatial features, we measure complexity of road networks using several area level…
Autonomous agents rely on sensor data to construct representations of their environments, essential for predicting future events and planning their actions. However, sensor measurements suffer from limited range, occlusions, and sensor…
Spatial data are often derived from multiple sources (e.g. satellites, in-situ sensors, survey samples) with different supports, but associated with the same properties of a spatial phenomenon of interest. It is common for predictors to…
Gaussian processes and random fields have a long history, covering multiple approaches to representing spatial and spatio-temporal dependence structures, such as covariance functions, spectral representations, reproducing kernel Hilbert…
Environmental and climate processes are often distributed over large space-time domains. Their complexity and the amount of available data make modelling and analysis a challenging task. Statistical modelling of environment and climate data…