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Title: Assessing and modelling extremal dependence in spatial extremes
Author: Kereszturi, Monika
ISNI:       0000 0004 6348 2190
Awarding Body: Lancaster University
Current Institution: Lancaster University
Date of Award: 2017
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Offshore structures, such as oil platforms and vessels, must be built such that they can withstand extreme environmental conditions (e.g., high waves and strong winds) that may occur during their lifetime. This means that it is essential to quantify probabilities of the occurrence of such extreme events. However, a difficulty arises in that there are very limited data available at these levels. The statistical field of extreme value theory provides asymptotically motivated models for extreme events, hence allowing extrapolation to very rare events. In addition to the risk to a single site, we are also interested in the joint risk of multiple offshore platforms being affected by the same extreme event. In order to understand joint extremal behaviour for two or more locations, the spatial dependence between the different locations must be considered. Extremal dependence between two locations can be of two types: asymptotic independence (AI) when the extremes at the two sites are unlikely to occur together, and asymptotic dependence (AD) when it is possible for both sites to be affected simultaneously. For finite samples it is often difficult to determine which type of dependence the data are more consistent with. In a large ocean basin it is reasonable to expect both of these features to be present, with some close by locations AD, with the dependence decreasing with distance, and some far apart locations AI. In this thesis we develop new diagnostic tools for distinguishing between AD and AI and illustrate these on North Sea wave height data. We also investigate how extremal dependence changes with direction and find evidence for spatial anisotropy in our data set. The most widely used spatial models assume asymptotic dependence or perfect independence between sites, which is often unrealistic in practice. Models that attempt to capture both AD and AI exist, but they are difficult to implement in practice due to their complexity and they are restricted in the forms of AD and AI they can model. In this thesis we introduce a family of bivariate distributions that exhibits all the required features of short, medium and long range extremal dependence required for pairwise dependence modelling in spatial applications.
Supervisor: Tawn, Jonathan ; Jonathan, Philip ; Fearnhead, Paul Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral