Inference for extreme values under threshold-based stopping rules

Abstract

There is a propensity for an extreme value analysis to be conducted as a consequence 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 its experiencing the UK's largest ever measured flow event in 2015. We show that without accounting for this stopping feature there would be substantial overdesign in response to the event.