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In environmental science applications, extreme events frequently exhibit a complex spatio-temporal structure, which is difficult to describe flexibly and estimate in a computationally efficient way using state-of-art parametric…

Methodology · Statistics 2022-12-22 Marco Oesting , Raphaël Huser

We investigate the predictability of extreme events in time series. The focus of this work is to understand under which circumstances large events are better predictable than smaller events. Therefore we use a simple prediction algorithm…

Data Analysis, Statistics and Probability · Physics 2008-01-30 S. Hallerberg , H. Kantz

Numerical climate models are complex and combine a large number of physical processes. They are key tools in quantifying the relative contribution of potential anthropogenic causes (e.g., the current increase in greenhouse gases) on high…

Applications · Statistics 2020-05-19 Anna Kiriliouk , Philippe Naveau

High accuracy complex computer models, or simulators, require large resources in time and memory to produce realistic results. Statistical emulators are computationally cheap approximations of such simulators. They can be built to replace…

Computation · Statistics 2016-08-25 Xiaoyu Liu , Serge Guillas

Computing the return times of extreme events and assessing the impact of climate change on such return times is fundamental to extreme event attribution studies. However, the rarity of such events in the observational record makes this task…

Atmospheric and Oceanic Physics · Physics 2024-12-03 Clément Le Priol , Joy M. Monteiro , Freddy Bouchet

Extreme events occur across the natural, engineering, and socioeconomic sciences, where rare but high-impact episodes can lead to disproportionate consequences that pose major challenges for prediction and risk management. Existing studies…

Dynamical Systems · Mathematics 2026-05-22 Charlotte Moser , Nan Chen , Marios Andreou

Extreme events, such as market crashes, natural disasters, and pandemics, are rare but catastrophic, often triggering cascading failures across interconnected systems. Accurate prediction and early warning can help minimize losses and…

Machine Learning · Computer Science 2025-06-10 Jingyi Gu , Xuan Zhang , Guiling Wang

Time Series Forecasting (TSF) is a widely researched topic with broad applications in weather forecasting, traffic control, and stock price prediction. Extreme values in time series often significantly impact human and natural systems, but…

Machine Learning · Computer Science 2023-10-12 Jincheng Wang , Yue Gao

Extreme events gain the attention of researchers due to their utmost importance in various contexts ranging from finance to climatology. This brings such recurrent events to the limelight of attention in interdisciplinary research. A…

Data Analysis, Statistics and Probability · Physics 2022-05-18 Sayantan Nag Chowdhury , Arnob Ray , Syamal K. Dana , Dibakar Ghosh

In this paper we describe a general framework for incorporating tidal uncertainty into probabilistic tsunami hazard assessment and propose the Pattern Method and a simpler special case called the $\Delta t$ Method as effective approaches.…

Numerical Analysis · Mathematics 2014-04-30 Loyce M. Adams , Randall J. LeVeque , Frank I. González

Extreme events, such as rogue waves, earthquakes and stock market crashes, occur spontaneously in many dynamical systems. Because of their usually adverse consequences, quantification, prediction and mitigation of extreme events are highly…

Chaotic Dynamics · Physics 2018-03-19 Mohammad Farazmand , Themistoklis P. Sapsis

Quantifying changes in the probability and magnitude of extreme flooding events is key to mitigating their impacts. While hydrodynamic data are inherently spatially dependent, traditional spatial models such as Gaussian processes are poorly…

Methodology · Statistics 2024-05-06 Reetam Majumder , Brian J. Reich , Benjamin A. Shaby

We propose a modification of a maximum likelihood procedure for tuning parameter values in models, based upon the comparison of their output to field data. Our methodology, which uses polynomial approximations of the sample space to…

Data Analysis, Statistics and Probability · Physics 2013-07-03 Nusret Balci , Juan M. Restrepo , Shankar C. Venkataramani

Projections of extreme sea levels (ESLs) are critical for managing coastal risks, but are made complicated by deep uncertainties. One key uncertainty is the choice of model structure used to estimate coastal hazards. Differences in model…

Data Analysis, Statistics and Probability · Physics 2020-06-15 Tony E. Wong , Travis Torline , Mingxuan Zhang

Dynamical systems with high intrinsic dimensionality are often characterized by extreme events having the form of rare transitions several standard deviations away from the mean. For such systems, order-reduction methods through projection…

Chaotic Dynamics · Physics 2018-07-04 Zhong Yi Wan , Pantelis R. Vlachas , Petros Koumoutsakos , Themistoklis P. Sapsis

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

Reliable estimates of sea level return levels are crucial for coastal flooding risk assessments and for coastal flood defence design. We describe a novel method for estimating extreme sea levels that is the first to capture seasonality,…

Applications · Statistics 2022-07-21 Eleanor D'Arcy , Jonathan A. Tawn , Amélie Joly , Dafni E. Sifnioti

Designs conditions for marine structures are typically informed by threshold-based extreme value analyses of oceanographic variables, in which excesses of a high threshold are modelled by a generalized Pareto (GP) distribution. Too low a…

Methodology · Statistics 2016-06-02 Paul Northrop , Nicolas Attalides , Philip Jonathan

The block maxima approach, which consists of dividing a series of observations into equal sized blocks to extract the block maxima, is commonly used for identifying and modelling extreme events using the generalized extreme value (GEV)…

Methodology · Statistics 2025-06-23 James H. McVittie , Orla A. Murphy

Predicting extreme events in chaotic systems, characterized by rare but intensely fluctuating properties, is of great importance due to their impact on the performance and reliability of a wide range of systems. Some examples include…

Data Analysis, Statistics and Probability · Physics 2024-06-17 Yuan Yuan , Adrian Lozano Duran