Related papers: Exploration and inference in spatial extremes usin…
Spatial statistics is concerned with the analysis of data that have spatial locations associated with them, and those locations are used to model statistical dependence between the data. The spatial data are treated as a single realisation…
Recent developments in extreme value statistics have established the so-called geometric approach as a powerful modelling tool for multivariate extremes. We tailor these methods to the case of spatial modelling and examine their efficacy at…
Understanding the spatial extent of extreme precipitation is necessary for determining flood risk and adequately designing infrastructure (e.g., stormwater pipes) to withstand such hazards. While environmental phenomena typically exhibit…
The analysis of extremal dependence in high dimensions has recently attracted considerable interest. Existing methodology primarily focuses on modeling and estimation of extremal dependence structures, often supported by concentration…
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…
The extremogram, proposed by Davis and Mikosch (2008), is a useful tool for measuring extremal dependence and checking model adequacy in a time series. We define the extremogram in the spatial domain when the data is observed on a lattice…
Modelling the extremal dependence structure of spatial data is considerably easier if that structure is stationary. However, for data observed over large or complicated domains, non-stationarity will often prevail. Current methods for…
A successful model for high-dimensional spatial extremes should, in principle, be able to describe both weakening extremal dependence at increasing levels and changes in the type of extremal dependence class as a function of the distance…
Spatial maps of extreme precipitation are crucial in flood protection. With the aim of producing maps of precipitation return levels, we propose a novel approach to model a collection of spatially distributed time series where the…
Extreme environmental events frequently exhibit spatial and temporal dependence. These data are often modeled using max stable processes (MSPs). MSPs are computationally prohibitive to fit for as few as a dozen observations, with supposed…
The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so…
Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…
Modeling nonstationarity that often prevails in extremal dependence of spatial data can be challenging, and typically requires bespoke or complex spatial models that are difficult to estimate. Inference for stationary and isotropic models…
The classical modeling of spatial extremes relies on asymptotic models (i.e., max-stable processes or $r$-Pareto processes) for block maxima or peaks over high thresholds, respectively. However, at finite levels, empirical evidence often…
Inference on the extremal behaviour of spatial aggregates of precipitation is important for quantifying river flood risk. There are two classes of previous approach, with one failing to ensure self-consistency in inference across different…
Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable…
Various natural phenomena exhibit spatial extremal dependence at short spatial distances. However, existing models proposed in the spatial extremes literature often assume that extremal dependence persists across the entire domain. This is…
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…
Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous…
With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial datasets. This has generated substantial interest over the last decade, already…