arXiv subjects

Callum J. R. Murphy-Barltrop

Publications and source records attributed to Callum J. R. Murphy-Barltrop.

3 recordsLinked to original sources

arXiv2026

A Geometric Framework for the Bayesian Estimation of Joint Environmental Extremes

Multivariate extreme events tend to have broader impacts on society compared to individual extremes. Flexible and accurate modeling of multivariate extremes is therefore crucial for many practical applications, including risk assessments and mitigation projects. In this work, we introduce a Bayesian modeling framework for bivariate extremes. Our approach utilizes the geometric extremes framework, for which data are decomposed into angular and radial components. The angular distribution is estimated using periodic M-splines, resulting in a natural circular density, while the radial distribution, conditional on the angles, is approximated using Bezier splines. The radial distribution also provides a means of estimating the limit set, the limiting shape of scaled sample clouds that encodes information pertaining to extremal dependence. Our Bayesian approach offers advantages over competing methods, particularly for uncertainty quantification and interpretation. Furthermore, our framework guarantees theoretical properties of limit sets, ensuring validity for inference. Notably, our model can be used to approximate extreme probabilities associated with failure sets in the joint tail, which are useful across many applications. We demonstrate the efficacy of our approach through numerical experiments and a case study on fire weather in Louisiana, USA, with diagnostics for the latter indicating strong model performance.

stat.ME↗

arXiv2025

Generative Machine Learning for Multivariate Angular Simulation

With the recent development of new geometric and angular-radial frameworks for multivariate extremes, reliably simulating from angular variables in moderate-to-high dimensions is of increasing importance. Empirical approaches have the benefit of simplicity, and work reasonably well in low dimensions, but as the number of variables increases, they can lack the required flexibility and scalability. Classical parametric models for angular variables, such as the von Mises--Fisher distribution (vMF), provide an alternative. Exploiting finite mixtures of vMF distributions increases their flexibility, but there are cases where, without letting the number of mixture components grow considerably, a mixture model with a fixed number of components is not sufficient to capture the intricate features that can arise in data. Owing to their flexibility, generative deep learning methods are able to capture complex data structures; they therefore have the potential to be useful in the simulation of multivariate angular variables. In this paper, we introduce a range of deep learning approaches for this task, including generative adversarial networks, normalizing flows and flow matching. We assess their performance via a range of metrics, and make comparisons to the more classical approach of using a finite mixture of vMF distributions. The methods are also applied to a metocean data set, with diagnostics indicating strong performance, demonstrating the applicability of such techniques to real-world, complex data structures.

stat.ML↗

arXiv2024

Deep Learning of Multivariate Extremes via a Geometric Representation

The study of geometric extremes, where extremal dependence properties are inferred from the deterministic limiting shapes of scaled sample clouds, provides an exciting approach to modelling the extremes of multivariate data. These shapes, termed limit sets, link together several popular extremal dependence modelling frameworks. Although the geometric approach is becoming an increasingly popular modelling tool, current inference techniques are limited to a low dimensional setting (d < 5), and generally require rigid modelling assumptions. In this work, we propose a range of novel theoretical results to aid with the implementation of the geometric extremes framework and introduce the first approach to modelling limit sets using deep learning. By leveraging neural networks, we construct asymptotically-justified yet flexible semi-parametric models for extremal dependence of high-dimensional data. We showcase the efficacy of our deep approach by modelling the complex extremal dependencies between meteorological and oceanographic variables in the North Sea off the coast of the UK.

stat.ME↗