# Inference for extreme values under threshold-based stopping rules

## TL;DR

This paper addresses biases in extreme value analysis caused by threshold-based stopping rules, proposing new likelihood-based methods to improve risk assessment accuracy, demonstrated through flood data analysis.

## Contribution

It introduces novel likelihood-based inference techniques that account for stopping rules, reducing bias and improving coverage in extreme value analysis.

## Key findings

- Stopping rules cause significant bias in extreme value estimates.
- New methods improve coverage probabilities in flood risk assessment.
- Application to river Lune data shows reduced over-design risk.

## Abstract

There is a propensity for an extreme value analyses to be conducted as a consequence of the occurrence of a large flooding event. This timing of the analysis introduces bias and poor coverage probabilities into the associated risk assessments and leads subsequently to inefficient flood protection schemes. We explore these problems through studying stochastic stopping criteria and propose new likelihood-based inferences that mitigate against these difficulties. Our methods are illustrated through the analysis of the river Lune, following it experiencing the UK's largest ever measured flow event in 2015. We show that without accounting for this stopping feature there would be substantial over-design in response to the event.