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We propose a Bayesian stochastic cellular automata modeling approach to model the spread of wildfires with uncertainty quantification. The model considers a dynamic neighborhood structure that allows neighbor states to inform transition…

Applications · Statistics 2023-06-07 Nicholas Grieshop , Christopher K. Wikle

Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…

Machine Learning · Statistics 2018-07-19 Leo L. Duan , Xia Wang , Rhonda D. Szczesniak

Spatio-temporal processes in environmental applications are often assumed to follow a Gaussian model, possibly after some transformation. However, heterogeneity in space and time might have a pattern that will not be accommodated by…

Applications · Statistics 2021-10-15 Thaís C. O. da Fonseca , Viviana G. R. Lobo , Alexandra M. Schmidt

This study presents a probabilistic surrogate model for localized wildfire spread based on a conditional flow matching algorithm. The approach models fire progression as a stochastic process by learning the conditional distribution of fire…

Machine Learning · Computer Science 2026-03-31 Bryan Shaddy , Haitong Qin , Brianna Binder , James Haley , Riya Duddalwar , Kyle Hilburn , Assad Oberai

Hawkes process is one of the most commonly used models for investigating the self-exciting nature of earthquake occurrences. However, seismicity patterns have complicated characteristics due to heterogeneous geology and stresses, for which…

Applications · Statistics 2023-02-15 Junhyeon Kwon , Yingcai Zheng , Mikyoung Jun

We present a general stochastic forest-fire model which shows a variety of different structures depending on the parameter values. The model contains three possible states per site (tree, burning tree, empty site) and three parameters (tree…

Condensed Matter · Physics 2009-10-22 B. Drossel , F. Schwabl

In agricultural landscapes, the composition and spatial configuration of cultivated and semi-natural elements strongly impact species dynamics, their interactions and habitat connectivity. To allow for landscape structural analysis and…

Populations and Evolution · Quantitative Biology 2020-03-05 Patrizia Zamberletti , Julien Papaïx , Edith Gabriel , Thomas Opitz

Joint modeling of spatially-oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes…

Methodology · Statistics 2021-03-22 Lu Zhang , Sudipto Banerjee , Andrew O. Finley

Gaussian processes (GPs) are important probabilistic tools for inference and learning in spatio-temporal modelling problems such as those in climate science and epidemiology. However, existing GP approximations do not simultaneously support…

Machine Learning · Computer Science 2021-06-21 Will Tebbutt , Arno Solin , Richard E. Turner

Cloud-to-ground lightning strikes observed in a specific geographical domain over time can be naturally modeled by a spatio-temporal point process. Our focus lies in the parametric estimation of its intensity function, incorporating both…

This paper presents a kriging method for spatial prediction of temporal intensity functions, for situations where a temporal point process is observed at different spatial locations. Assuming that several replications of the processes are…

Methodology · Statistics 2021-07-02 Daniel Gervini

Recent crash frequency studies incorporate spatiotemporal correlations, but these studies have two key limitations: i) none of these studies accounts for temporal variation in model parameters; and ii) Gibbs sampler suffers from convergence…

Applications · Statistics 2020-08-11 Prasad Buddhavarapu , Prateek Bansal , Jorge A. Prozzi

Spatial modelling of extreme values allows studying the risk of joint occurrence of extreme events at different locations and is of significant interest in climatic and other environmental sciences. A popular class of dependence models for…

Methodology · Statistics 2026-02-11 Lorenzo Dell'Oro , Carlo Gaetan , Thomas Opitz

Due to severe societal and environmental impacts, wildfire prediction using multi-modal sensing data has become a highly sought-after data-analytical tool by various stakeholders (such as state governments and power utility companies) to…

Applications · Statistics 2023-10-12 Chen Xu , Yao Xie , Daniel A. Zuniga Vazquez , Rui Yao , Feng Qiu

Forest fire spreading is a complex phenomenon characterized by a stochastic behavior. Nowadays, the enormous quantity of georeferenced data and the availability of powerful techniques for their analysis can provide a very careful picture of…

Populations and Evolution · Quantitative Biology 2023-09-06 Roberto Beneduci , Giovanni Mascali

Existing spatio-temporal Hawkes process models typically rely on either parametric or semiparametric assumptions, limiting the model's ability to capture complex endogenous and exogenous event dynamics. We propose a fully Bayesian…

Methodology · Statistics 2026-03-31 Wenqing Liu , Xenia Miscouridou , Déborah Sulem

Due to climate change and human activity, wildfires are expected to become more frequent and extreme worldwide, causing economic and ecological disasters. The deployment of preventive measures and operational forecasts can be aided by…

Applications · Statistics 2020-02-28 Thomas Opitz , Florent Bonneu , Edith Gabriel

We propose a Multivariate Spatio-Temporal Neural Hawkes Process for modeling complex multivariate event data with spatio-temporal dynamics. The proposed model extends continuous-time neural Hawkes processes by integrating spatial…

Machine Learning · Statistics 2026-03-03 Christopher Chukwuemeka , Hojun You , Mikyoung Jun

Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field…

Dynamical Systems · Mathematics 2021-05-20 Denis D. Patterson , Simon A. Levin , A. Carla Staver , Jonathan D. Touboul

We develop a spatio-temporal model to forecast sensor output at five locations in North East England. The signal is described using coupled dynamic linear models, with spatial effects specified by a Gaussian process. Data streams are…

Applications · Statistics 2018-06-15 Yingying Lai , Andrew Golightly , Richard Boys