Related papers: ABC model selection for spatial extremes models ap…
In many applications involving spatial point patterns, we find evidence of inhibition or repulsion. The most commonly used class of models for such settings are the Gibbs point processes. A recent alternative, at least to the statistical…
Model selection in the presence of intractable likelihoods remains a central challenge in Bayesian inference. Approximate Bayesian computation (ABC) provides a flexible likelihood-free framework, but its use for model choice is known to be…
Approximate Bayesian Computation (ABC) methods have gained in their popularity over the last decade because they expand the horizon of Bayesian parameter inference methods to the range of models for which only forward simulation is…
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…
The modeling of spatio-temporal trends in temperature extremes can help better understand the structure and frequency of heatwaves in a changing climate. Here, we study annual temperature maxima over Southern Europe using a century-spanning…
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…
Since many environmental processes such as heat waves or precipitation are spatial in extent, it is likely that a single extreme event affects several locations and the areal modelling of extremes is therefore essential if the spatial…
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…
Precipitation exceedance probabilities are widely used in engineering design, risk assessment, and floodplain management. While common approaches like NOAA Atlas 14 assume that extreme precipitation characteristics are stationary over time,…
Max-stable processes are the natural analogues of the generalized extreme-value distribution for the modelling of extreme events in space and time. Under suitable conditions, these processes are asymptotically justified models for maxima of…
Approximate Bayesian Computation (ABC) has become one of the major tools of likelihood-free statistical inference in complex mathematical models. Simultaneously, stochastic differential equations (SDEs) have developed to an established tool…
Statistical extreme value theory is concerned with the use of asymptotically motivated models to describe the extreme values of a process. A number of commonly used models are valid for observed data that exceed some high threshold.…
Spatially isotropic max-stable processes have been used to model extreme spatial or space-time observations. One prominent model is the Brown-Resnick process, which has been successfully fitted to time series, spatial data and space-time…
A computationally simple approach to inference in state space models is proposed, using approximate Bayesian computation (ABC). ABC avoids evaluation of an intractable likelihood by matching summary statistics for the observed data with…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. One such representation is based on a limit of…
Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits…
Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes simulation highly nontrivial. Algorithms based on finite…
Recent extreme value theory literature has seen significant emphasis on the modelling of spatial extremes, with comparatively little consideration of spatio-temporal extensions. This neglects an important feature of extreme events: their…
Approximate Bayesian computation (ABC) is commonly used for parameter estimation and model comparison for intractable simulator-based models whose likelihood function cannot be evaluated. In this paper we instead investigate the feasibility…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. For statistical inference it is often assumed that…