arXiv subjects

Ilaria Prosdocimi

Publications and source records attributed to Ilaria Prosdocimi.

5 recordsLinked to original sources

arXiv2026

A lightweight framework for characterising extreme precipitation events in climate ensembles

This article summarises the methods used by the team ``Ca' Foscari" for the EVA 2025 Data Challenge. The questions of the challenge concern the estimation of exceedance probabilities across several locations. Rather than modelling the spatial dependence structure, we reduce the problems to univariate ones by considering relevant spatial order statistics across the sites. Within a Peaks over Threshold framework, we model the marginal distributions of exceedances using generalised Pareto distributions. Generalised additive models are employed to allow the parameters to vary as functions of external predictors, which for all questions are reduced to the month. For questions 1 and 2, the required estimates and confidence intervals are obtained by generating samples from our fitted models. Question 3 involves the dependence between two consecutive observed statistics. To account for this temporal dependence, we fit a conditional extreme value model and derive empirical estimates of persistent extreme events by simulating from this model.

stat.ME↗

arXiv2026

Orthogonal parametrisations of Extreme-Value distributions

Extreme value distributions are routinely employed to assess risks connected to extreme events in a large number of applications. They typically are two- or three- parameter distributions: the inference can be unstable, which is particularly problematic given the fact that often times these distributions are fitted to small samples. Furthermore, the distribution's parameters are generally not directly interpretable and not the key aim of the estimation. We present several orthogonal reparametrisations of the main extreme-value distributions, key in the modelling of rare events. In particular, we apply the theory developed in Cox and Reid (1987) to the Generalised Extreme-Value, Generalised Pareto, and Gumbel distributions. We illustrate the principal advantage of these reparametrisations in a simulation study.

math.ST↗

arXiv2025

Non-stationarities in extreme hourly precipitation over the Piave Basin, northern Italy

We study the spatio-temporal features of extremal sub-daily precipitation data over the Piave river basin in northeast Italy using a rich database of observed hourly rainfall. Empirical evidence suggests that both the marginal and dependence structures for extreme precipitation in the area exhibit seasonal patterns, and spatial dependence appears to weaken as events become more extreme. We investigate factors affecting the marginal distributions, the spatial dependence and the interplay between them. Capturing these features is essential to provide a realistic description of extreme precipitation processes in order to better estimate their associated risks. With this aim, we identify various climatic covariates at different spatio-temporal scales and explore their usefulness. We go beyond existing literature by investigating and comparing the performance of recently proposed covariate-dependent models for both the marginal and dependence structures of extremes. Furthermore, a flexible max-id model, which encompasses both asymptotic dependence and independence, is used to learn about the spatio-temporal variability of rainfall processes at extreme levels. We find that modelling non-stationarity only at the marginal level does not fully capture the variability of precipitation extremes, and that it is important to also capture the seasonal variation of extremal dependence.

stat.AP↗

arXiv2025

Robust and efficient estimation for the Generalized Extreme-Value distribution with application to flood frequency analysis in the UK

A common approach for modeling extremes, such as peak flow or high temperatures, is the three-parameter Generalized Extreme-Value distribution. This is typically fit to extreme observations, here defined as maxima over disjoint blocks. This results in limited sample sizes and consequently, the use of classic estimators, such as the maximum likelihood estimator, may be inappropriate, as they are highly sensitive to outliers. To address these limitations, we propose a novel robust estimator based on the minimization of the density power divergence, controlled by a tuning parameter $\alpha$ that balances robustness and efficiency. When $\alpha = 0$, our estimator coincides with the maximum likelihood estimator; when $\alpha = 1$, it corresponds to the $L^2$ estimator, known for its robustness. We establish convenient theoretical properties of the proposed estimator, including its asymptotic normality and the boundedness of its influence function for $\alpha > 0$. The practical efficiency of the method is demonstrated through empirical comparisons with the maximum likelihood estimator and other robust alternatives. Finally, we illustrate its relevance in a case study on flood frequency analysis in the UK and provide some general conclusions in Section 6.

stat.AP↗

arXiv2025

Bayesian Mixture Models for Heterogeneous Extremes

The conventional use of the Generalized Extreme Value (GEV) distribution to model block maxima may be inappropriate when extremes are actually structured into multiple heterogeneous groups. In this work, we propose a novel approach for describing the behavior of extreme values in the presence of such heterogeneity. Rather than defaulting to the GEV distribution simply because it arises as a theoretical limit, we show that alternative block maxima-based models can also align with the extremal types theorem while providing improved flexibility in practice. Our formulation leads us to a mixture model that has a Bayesian nonparametric interpretation as a Dirichlet process mixture of GEV distributions. The use of an infinite number of components enables the characterization of every possible block behavior, while at the same time capturing similarities between observations based on their extremal behavior. By employing a Dirichlet process prior on the mixing measure, we can capture the complex structure of the data without the need to pre-specify the number of mixture components. The application of the proposed model is illustrated using both simulated and real-world data.

stat.ME↗