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Spatial processes observed in various fields, such as climate and environmental science, often occur on a large scale and demonstrate spatial nonstationarity. Fitting a Gaussian process with a nonstationary Mat\'ern covariance is…

Machine Learning · Statistics 2023-06-21 Pratik Nag , Yiping Hong , Sameh Abdulah , Ghulam A. Qadir , Marc G. Genton , Ying Sun

One of the goals of climate science is to characterize the statistics of extreme and potentially dangerous events in the present and future climate. Extreme events like heat waves, droughts, or floods due to persisting rains are…

Atmospheric and Oceanic Physics · Physics 2020-01-08 Francesco Ragone , Freddy Bouchet

We introduce a Gaussian process-based model for handling of non-stationarity. The warping is achieved non-parametrically, through imposing a prior on the relative change of distance between subsequent observation inputs. The model allows…

Machine Learning · Statistics 2019-12-06 David Tolpin

Obtaining high-resolution maps of precipitation data can provide key insights to stakeholders to assess a sustainable access to water resources at urban scale. Mapping a nonstationary, sparse process such as precipitation at very high…

Applications · Statistics 2023-02-08 Jiachen Zhang , Matthew Bonas , Diogo Bolster , Geir-Arne Fuglstad , Stefano Castruccio

Stochastic reduced models are an important tool in climate systems whose many spatial and temporal scales cannot be fully discretized or underlying physics may not be fully accounted for. One form of reduced model, the linear inverse model…

Methodology · Statistics 2020-04-29 Dallas Foster , Darin Comeau , Nathan M. Urban

In this study, we introduce a novel and comprehensive extension of a Bayesian spatio-temporal disease mapping model that explicitly accounts for gender-specific effects of meteorological exposures. Leveraging fine-scale weekly mortality and…

Applications · Statistics 2025-07-18 Corinna Perchtold , Julia Eisenberg , Philipp Otto

Nonstationarity is a major challenge in analyzing spatial data. For example, daily precipitation measurements may have increased variability and decreased spatial smoothness in areas with high mean rainfall. Common nonstationary covariance…

Methodology · Statistics 2019-05-31 Geoffrey Colin Lee Peterson , Joseph Guinness , Adam Terando , Brian J. Reich

Inverse problems with spatiotemporal observations are ubiquitous in scientific studies and engineering applications. In these spatiotemporal inverse problems, observed multivariate time series are used to infer parameters of physical or…

Methodology · Statistics 2022-04-26 Shiwei Lan , Shuyi Li , Mirjeta Pasha

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 introduce a framework for updating large scale geospatial processes using a model-data synthesis method based on Bayesian hierarchical modelling. Two major challenges come from updating large-scale Gaussian process and modelling…

Applications · Statistics 2018-05-01 Zhe Sha , Jonathan Rougier , Maike Schumacher , Jonathan Bamber

Mixed modeling of extreme values and random effects is relatively unexplored topic. Computational difficulties in using the maximum likelihood method for mixed models and the fact that maximum likelihood method uses available data and does…

Applications · Statistics 2019-07-05 Ali Reza Fotouhi

Understanding and mapping extreme heat is critical for risk management and public health planning, particularly in regions with complex terrain and heterogeneous climate. We present a case study of extreme heat in the Four Corners region of…

Applications · Statistics 2026-04-22 Ben Seiyon Lee , Reetam Majumder , Jordan Richards , Emma S. Simpson , Likun Zhang

Bayesian models based on Gaussian processes (GPs) offer a flexible framework to predict spatially distributed variables with uncertainty. But the use of nonstationary priors, often necessary for capturing complex spatial patterns, makes…

Machine Learning · Statistics 2025-06-02 Gabriel V Cardoso , Mike Pereira

Generative modeling of spatio-temporal fields is crucial for a variety of applications, including stochastic weather generators and climate-model surrogates. However, many such fields exhibit complex dependence structures that vary across…

Methodology · Statistics 2026-05-06 Carrie J. Lei-Cramer , Jian Cao , Matthias Katzfuss

Earth's temperature variability can be partitioned into internal and externally-forced components. Yet, underlying mechanisms and their relative contributions remain insufficiently understood, especially on decadal to centennial timescales.…

Atmospheric and Oceanic Physics · Physics 2023-02-01 Maybritt Schillinger , Beatrice Ellerhoff , Robert Scheichl , Kira Rehfeld

We present a new approach to modeling the future development of extreme temperatures globally and on a long time-scale by using non-stationary generalized extreme value distributions in combination with logistic functions. This approach is…

Atmospheric and Oceanic Physics · Physics 2022-07-28 Justus Contzen , Thorsten Dickhaus , Gerrit Lohmann

Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…

Computation · Statistics 2020-02-18 Andrew Zammit-Mangion , Jonathan Rougier

Local climate information is crucial for impact assessment and decision-making, yet coarse global climate simulations cannot capture small-scale phenomena. Current statistical downscaling methods infer these phenomena as temporally…

Machine Learning · Computer Science 2025-09-24 Jonathan Schmidt , Luca Schmidt , Felix Strnad , Nicole Ludwig , Philipp Hennig

Earth System Models (ESMs) are the state of the art for projecting the effects of climate change. However, longstanding uncertainties in their ability to simulate regional and local precipitation extremes and related processes inhibit…

Applications · Statistics 2017-07-20 Evan Kodra , Singdhansu Chatterjee , Stone Chen , Auroop R. Ganguly

We introduce a Bayesian approach for multivariate spatio-temporal prediction for high-dimensional count-valued data. Our primary interest is when there are possibly millions of data points referenced over different variables, geographic…

Methodology · Statistics 2015-12-24 Jonathan R. Bradley , Scott H. Holan , Christopher K. Wikle