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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

Weather extremes produce major impacts on society and ecosystems and are likely to change in likelihood and magnitude with climate change. However, very low probability events are hard to characterize statistically using observations or…

Applications · Statistics 2026-04-28 Christopher J. Paciorek , Daniel Cooley

Changing climate signals and the continuous world population growth requires proper hydrologic risk analysis to build and operate water resource infrastructures in a sustainable way. Although modernized computational facilities are becoming…

Pattern Formation and Solitons · Physics 2022-08-30 Victor Peñaranda , David Serrano , Mahesh Maskey

Climate models have become an important tool in the study of climate and climate change, and ensemble experiments consisting of multiple climate-model runs are used in studying and quantifying the uncertainty in climate-model output.…

Applications · Statistics 2011-04-15 Stephan R. Sain , Reinhard Furrer , Noel Cressie

We propose a Bayesian hierarchical model for spatial extremes on a large domain. In the data layer a Gaussian elliptical copula having generalized extreme value (GEV) marginals is applied. Spatial dependence in the GEV parameters are…

Rain precipitation prediction is a challenging task as it depends on weather and meteorological features which vary from location to location. As a result, a prediction model that performs well at one location does not perform well at other…

Flexible spatial models that allow transitions between tail dependence classes have recently appeared in the literature. However, inference for these models is computationally prohibitive, even in moderate dimensions, due to the necessity…

Statistics Theory · Mathematics 2020-12-03 Likun Zhang , Benjamin A. Shaby , Jennifer L. Wadsworth

Forecasting extreme precipitation is essential yet challenging due to its rarity and complexity. We develop a large deviation framework to estimate the return times of extreme precipitation events. We first find that the Landau…

Statistical Mechanics · Physics 2026-04-14 Haotian Xie , Haoxian Liu , Jingfang Fan , Ying Tang

Max-stable processes have been expanded to quantify extremal dependence in spatio-temporal data. Due to the interaction between space and time, spatio-temporal data are often complex to analyze. So, characterizing these dependencies is one…

Methodology · Statistics 2019-05-21 Abdul-Fattah Abu-Awwad , Véronique Maume-Deschamps , Pierre Ribereau

Accurate static traffic assignment models are important tools for the assessment of strategic transportation policies. In this article we present a novel approach to partition road networks through network modularity to produce data-driven…

Systems and Control · Electrical Eng. & Systems 2022-11-28 Alexander Roocroft , Giuliano Punzo , Muhamad Azfar Ramli

Deep learning models have achieved remarkable progress in precipitation prediction. However, they still face significant challenges in accurately capturing spatial details of radar images, particularly in regions of high precipitation…

Computer Vision and Pattern Recognition · Computer Science 2025-03-26 Li Chaorong , Ling Xudong , Yang Qiang , Qin Fengqing , Huang Yuanyuan

The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…

Probability · Mathematics 2015-09-03 Helena Ferreira , Luísa Pereira , Ana Paula Martins

Accurate forecasting of extreme weather events such as heavy rainfall or storms is critical for risk management and disaster mitigation. Although high-resolution radar observations have spurred extensive research on nowcasting models,…

Machine Learning · Computer Science 2026-02-09 Changhoon Song , Teng Yuan Chang , Youngjoon Hong

Partition-wise models offer a flexible approach for modeling complex and multidimensional data that are capable of producing interpretable results. They are based on partitioning the observed data into regions, each of which is modeled with…

Methodology · Statistics 2017-06-07 Rex C. Y. Cheung , Alexander Aue , Thomas C. M. Lee

In many insurance contexts, dependence between risks of a portfolio may arise from their frequencies. We investigate a dependent risk model in which we assume the vector of count variables to be a tree-structured Markov random field with…

Methodology · Statistics 2026-02-03 Hélène Cossette , Benjamin Côté , Alexandre Dubeau , Etienne Marceau

We consider daily rainfall observations at 32 stations in the province of North Holland (the Netherlands) during 30 years. Let $T$ be the total rainfall in this area on one day. An important question is: what is the amount of rainfall $T$…

Applications · Statistics 2008-07-28 T. A. Buishand , L. de Haan , C. Zhou

There is substantial empirical and climatological evidence that precipitation extremes have become more extreme during the twentieth century, and that this trend is likely to continue as global warming becomes more intense. However,…

Motivated by the analysis of extreme rainfall data, we introduce a general Bayesian hierarchical model for estimating the probability distribution of extreme values of intermittent random sequences, a common problem in geophysical and…

Methodology · Statistics 2020-05-26 Enrico Zorzetto , Antonio Canale , Marco Marani

Rainfall exhibits extreme variability at many space and time scales and calls for a statistical description. Based on an analysis of radar measurements of precipitation over the tropical oceans, we introduce a new probability law for the…

Atmospheric and Oceanic Physics · Physics 2015-09-30 Prasun K. Kundu , Ravi K. Siddani

Joint models are a common and important tool in the intersection of machine learning and the physical sciences, particularly in contexts where real-world measurements are scarce. Recent developments in rainfall-runoff modeling, one of the…

Machine Learning · Computer Science 2019-11-22 Guy Shalev , Ran El-Yaniv , Daniel Klotz , Frederik Kratzert , Asher Metzger , Sella Nevo