TY - JOUR

T1 - Extreme value methods for estimating rare events in Utopia

T2 - EVA (2023) Conference Data Challenge: Team Lancopula Utopiversity

AU - André, Lídia

AU - Campbell, Ryan

AU - Farrell, Aiden

AU - D’Arcy, Eleanor

AU - Healy, Daire

AU - Kakampakou, Lydia

AU - Murphy, Conor

AU - Murphy-Barltrop, Callum John Rowlandson

AU - Speers, Matthew

PY - 2025/3/1

Y1 - 2025/3/1

N2 - To capture the extremal behaviour of complex environmental phenomena in practice, flexible 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 probabilities. For challenge C3, we propose an extension of available models in the multivariate literature and use this framework to estimate joint 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.

AB - To capture the extremal behaviour of complex environmental phenomena in practice, flexible 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 probabilities. For challenge C3, we propose an extension of available models in the multivariate literature and use this framework to estimate joint 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.

KW - 62G32

KW - Extremal dependence

KW - Generalised additive modelling

KW - Non-stationary extremes

KW - Peaks-over-threshold modelling

U2 - 10.1007/s10687-024-00498-w

DO - 10.1007/s10687-024-00498-w

M3 - Journal article

C2 - 40242571

VL - 28

SP - 23

EP - 45

JO - Extremes

JF - Extremes

SN - 1572-915X

IS - 1

ER -