Attalides, N; (2015) Threshold-based extreme value modelling. Doctoral thesis , UCL (University College London).

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Abstract

There are numerous benefits of analysing and understanding extreme events. More specifically, quantifying the uncertainty of rare environmental extremes has been of great concern for a variety of stakeholders such as insurance companies and governments. What is more, the practical implications of extreme weather events like hurricanes and floods pose a need for engineers to design structures that can be exposed to these conditions and withstand them for many years in the future. It is not surprising therefore that statistical modelling of extremes, in its own right, has been playing an important role in the design process. This thesis aims to contribute to the extreme value analysis literature primarily in the area concerned with threshold-based extreme value modelling. The major focus is on developing methods for selecting an appropriate threshold and on accounting for the uncertainty in this selection. For much of the thesis, Bayesian methods of inference are used and although the thesis concentrates on environmental applications, the methodology proposed can be applied in a more general context. We introduce univariate extreme value theory and in particular the statistical methods employed to make inferences using extreme value models. In addition, we examine the intricacies of Bayesian inference and through a simulation study compare different prior distributions based on predictive inferences for future extreme values. For the “standard” independent and identically distributed (i.i.d.) observations we propose a Bayesian cross-validation method for selecting the threshold and use Bayesian model averaging to combine inferences from different thresholds. We extend this approach to the case where independence is considered as an unrealistic assumption and explore threshold specification in extreme value regression modelling.

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