arXiv subjects

C. J. R. Murphy-Barltrop

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

6 recordsLinked to original sources

arXiv2026

Exploring climate change effects on concurrent floods and concurrent droughts via statistical deep learning

Concurrent floods and concurrent droughts in nearby catchments pose challenges to risk assessment and water management. Climate change is affecting extremely high and low discharge, but the complex interplay between changes in individual catchments and in the dependence across catchments make it difficult to provide accurate assessments of the occurrence probabilities of concurrent extremes. In this work, we use a contemporary statistical deep learning model (the deep SPAR framework) to capture concurrent river floods and droughts in four catchments in the Upper Danube basin, based on discharge simulated by a hydrological model driven with large ensemble climate model output. The statistical model is able to accurately capture the multivariate extremes of the simulated discharge, which we assess by making use of the large available sample size. We subsequently use our statistical model to study changes in joint tail behaviour of discharge over time, finding that both compound flooding and drought-like conditions are becoming increasingly likely towards the end of the 21st century under a high-emission scenario. In particular, our results highlight that changes in the dependence structure of extremes strongly contribute to the detected changes, an aspect that would be difficult to capture with traditional approaches. This work paves the way for highly flexible, general inference on compound extremes in hydrological applications, and demonstrates key advantages of using statistical deep learning in this setting.

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arXiv2025

Modelling non-stationary extremal dependence through a geometric approach

Non-stationary extremal dependence, whereby the relationship between the extremes of multiple variables evolves over time, is commonly observed in many environmental and financial data sets. However, most multivariate extreme value models are only suited to stationary data. A recent approach to multivariate extreme value modelling uses a geometric framework, whereby extremal dependence features are inferred through the limiting shapes of scaled sample clouds. This framework can capture a wide range of dependence structures, and a variety of inference procedures have been proposed in the stationary setting. In this work, we first extend the geometric framework to the non-stationary setting and outline assumptions to ensure the necessary convergence conditions hold. We then introduce a flexible, semi-parametric modelling framework for obtaining estimates of limit sets in the non-stationary setting. Through rigorous simulation studies, we demonstrate that our proposed framework can capture a wide range of dependence forms and is robust to different model formulations. We illustrate the proposed methods on financial returns data and present several practical uses.

stat.ME↗

arXiv2024

Improving estimation for asymptotically independent bivariate extremes via global estimators for the angular dependence function

Modelling the extremal dependence of bivariate variables is important in a wide variety of practical applications, including environmental planning, catastrophe modelling and hydrology. The majority of these approaches are based on the framework of bivariate regular variation, and a wide range of literature is available for estimating the dependence structure in this setting. However, such procedures are only applicable to variables exhibiting asymptotic dependence, even though asymptotic independence is often observed in practice. In this paper, we consider the so-called `angular dependence function'; this quantity summarises the extremal dependence structure for asymptotically independent variables. Until recently, only pointwise estimators of the angular dependence function have been available. We introduce a range of global estimators and compare them to another recently introduced technique for global estimation through a systematic simulation study, and a case study on river flow data from the north of England, UK.

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arXiv2024

Extreme value methods for estimating rare events in Utopia

To capture the extremal behaviour of complex environmental phenomena in practice, flexi\-ble techniques for modelling tail behaviour are required. In this paper, we introduce a variety of such methods, which were used by the Lancopula Utopiversity team to tackle the EVA (2023) Conference Data Challenge. This data challenge was split into four challenges, labelled C1-C4. Challenges C1 and C2 comprise univariate problems, where the goal is to estimate extreme quantiles for a non-stationary time series exhibiting several complex features. For these, we propose a flexible modelling technique, based on generalised additive models, with diagnostics indicating generally good performance for the observed data. Challenges C3 and C4 concern multivariate problems where the focus is on estimating joint extremal probabilities. For challenge C3, we propose an extension of available models in the multivariate literature and use this framework to estimate extreme probabilities in the presence of non-stationary dependence. Finally, for challenge C4, which concerns a 50 dimensional random vector, we employ a clustering technique to achieve dimension reduction and use a conditional modelling approach to estimate extremal probabilities across independent groups of variables.

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arXiv2024

Modelling non-stationarity in asymptotically independent extremes

In many practical applications, evaluating the joint impact of combinations of environmental variables is important for risk management and structural design analysis. When such variables are considered simultaneously, non-stationarity can exist within both the marginal distributions and dependence structure, resulting in complex data structures. In the context of extremes, few methods have been proposed for modelling trends in extremal dependence, even though capturing this feature is important for quantifying joint impact. Moreover, most proposed techniques are only applicable to data structures exhibiting asymptotic dependence. Motivated by observed dependence trends of data from the UK Climate Projections, we propose a novel semi-parametric modelling framework for bivariate extremal dependence structures. This framework allows us to capture a wide variety of dependence trends for data exhibiting asymptotic independence. When applied to the climate projection dataset, our model detects significant dependence trends in observations and, in combination with models for marginal non-stationarity, can be used to produce estimates of bivariate risk measures at future time points.

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arXiv2022

New estimation methods for extremal bivariate return curves

In the multivariate setting, estimates of extremal risk measures are important in many contexts, such as environmental planning and structural engineering. In this paper, we propose new estimation methods for extremal bivariate return curves, a risk measure that is the natural bivariate extension to a return level. Unlike several existing techniques, our estimates are based on bivariate extreme value models that can capture both key forms of extremal dependence. We devise tools for validating return curve estimates, as well as representing their uncertainty, and compare a selection of curve estimation techniques through simulation studies. We apply the methodology to two metocean data sets, with diagnostics indicating generally good performance.

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