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It is no secret that statistical modelling often involves making simplifying assumptions when attempting to study complex stochastic phenomena. Spatial modelling of extreme values is no exception, with one of the most common such…

Applications · Statistics 2025-05-05 Lydia Kakampakou , Emma S. Simpson , Jennifer L. Wadsworth

Predicting the response at an unobserved location is a fundamental problem in spatial statistics. Given the difficulty in modeling spatial dependence, especially in non-stationary cases, model-based prediction intervals are at risk of…

Methodology · Statistics 2025-07-09 Huiying Mao , Ryan Martin , Brian Reich

Ambient air pollution measurements from regulatory monitoring networks are routinely used to support epidemiologic studies and environmental policy decision making. However, regulatory monitors are spatially sparse and preferentially…

Applications · Statistics 2026-03-02 Wenlong Gong , Brian J. Reich , Joseph Guinness

Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…

Statistics Theory · Mathematics 2019-01-29 Nan Chen , Andrew J. Majda , Xin T. Tong

We construct a Gaussian random field (GRF) that combines fractional smoothness with spatially varying anisotropy. The GRF is defined through a stochastic partial differential equation (SPDE), where the range, marginal variance, and…

Methodology · Statistics 2025-12-23 Elling Svee , Geir-Arne Fuglstad

Empirical modelling often aims for the simplest model consistent with the data. A new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space. As is well-known, traditional…

Chaotic Dynamics · Physics 2009-11-10 Patrick E. McSharry , Leonard A. Smith

In many practical applications, evaluating the joint impact of combinations of environmental variables is important for risk management and structural design analysis. When such variables are considered simultaneously, non-stationarity can…

Applications · Statistics 2024-04-23 C. J. R. Murphy-Barltrop , J. L. Wadsworth

In this paper, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher dimensional spaces, transforming and clarifying…

Methodology · Statistics 2013-01-22 Luke Bornn , Gavin Shaddick , James V Zidek

Modeling the joint distribution of extreme weather events in multiple locations is a challenging task with important applications. In this study, we use max-stable models to study extreme daily precipitation events in Switzerland. The…

Methodology · Statistics 2018-11-29 Clément Chevalier , David Ginsbourger , Olivia Martius

We study the spatio-temporal features of extremal sub-daily precipitation data over the Piave river basin in northeast Italy using a rich database of observed hourly rainfall. Empirical evidence suggests that both the marginal and…

Applications · Statistics 2025-11-26 Dáire Healy , Ilaria Prosdocimi , Isadora Antoniano-Villalobos

Extreme events over large spatial domains may exhibit highly heterogeneous tail dependence characteristics, yet most existing spatial extremes models yield only one dependence class over the entire spatial domain. To accurately characterize…

Methodology · Statistics 2025-11-14 Muyang Shi , Likun Zhang , Mark D. Risser , Benjamin A. Shaby

We introduce a novel class of non-stationary covariance functions for random fields on linear networks that allows both the variance and the correlation range of the random field to vary spatially. The proposed covariance functions are…

Statistics Theory · Mathematics 2026-02-23 Alfredo Alegría

Paradoxically, while the assumptions of second-order stationarity and isotropy appear outdated in light of modern spatial data, they remain remarkably robust in practice, as nonstationary methods often provide marginal improvements in…

Methodology · Statistics 2025-11-07 Federico Blasi , Reinhard Furrer

The use of geospatially dependent information, which has been stipulated as a law in geography, to model geographic patterns forms the cornerstone of geostatistics, and has been inherited in many data science based techniques as well, such…

Applications · Statistics 2025-05-05 Jon Wang , Meng Lu

Standard geostatistical models assume second order stationarity of the underlying Random Function. In some instances, there is little reason to expect the spatial dependence structure to be stationary over the whole region of interest. In…

Methodology · Statistics 2014-12-04 Francky Fouedjio , Nicolas Desassis , Jacques Rivoirard

We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different…

Machine Learning · Computer Science 2019-06-28 Nguyen Q. Tran , Oleksii Abramenko , Alexander Jung

In spatial statistics, it is often assumed that the spatial field of interest is stationary and its covariance has a simple parametric form, but these assumptions are not appropriate in many applications. Given replicate observations of a…

Methodology · Statistics 2020-12-14 Brian Kidd , Matthias Katzfuss

Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and…

Machine Learning · Statistics 2015-07-10 Chintan A. Dalal , Vladimir Pavlovic , Robert E. Kopp

With the widespread availability of satellite-based instruments, many geophysical processes are measured on a global scale and they often show strong nonstationarity in the covariance structure. In this paper we present a flexible class of…

Applications · Statistics 2009-01-27 Mikyoung Jun , Michael L. Stein

The construction of valid and flexible cross-covariance functions is a fundamental task for modeling multivariate space-time data arising from climatological and oceanographical phenomena. Indeed, a suitable specification of the covariance…

Statistics Theory · Mathematics 2017-11-23 Alfredo Alegría , Emilio Porcu , Reinhard Furrer , Jorge Mateu