# Extreme value methods for estimating rare events in Utopia: EVA (2023) conference data challenge: team Lancopula Utopiversity

## TL;DR

This paper presents methods for modeling rare extreme events in environmental data using flexible statistical techniques.

## Contribution

The paper introduces novel approaches for univariate and multivariate extreme value analysis, including generalized additive models and clustering for dimension reduction.

## Key findings

- Generalized additive models performed well for estimating extreme quantiles in non-stationary time series.
- An extended multivariate model was used to estimate joint probabilities with non-stationary dependence.
- Clustering and conditional modeling effectively estimated extremal probabilities in high-dimensional data.

## Abstract

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.

The online version contains supplementary material available at 10.1007/s10687-024-00498-w.