There are many real-life situations where we might want to know the chance that a rare event will occur. For instance, if we were interested in the building of flood defences, we would want to take into account the amount of rainfall that the construction should be able to withstand, and knowing how often particularly bad rainfall events are likely to occur would be an important design consideration. Often with rare situations, it may be the case that we are interested in an event that has never happened before, making modelling a huge challenge. The area of statistics known as extreme value theory is dedicated to studying rare events such as these, and allows the development of techniques that are robust to the fact that there is an intrinsically limited amount of data available concerning these infrequent events.
The main aim of my PhD project is to develop techniques related to extreme value theory where there are multiple variables to consider, and of particular interest is developing models that can encapsulate the various ways that these different variables may affect one another. This aim will be achieved by drawing on methods from other areas of statistics, particularly graphical models and vine copulae, which are used to capture underlying dependence structures between variables.
An important consideration when modelling multivariate extreme events is whether there is asymptotic independence or asymptotic dependence between the variables. In the EVT literature, there are currently methods available that can be applied when we have extremes occurring in all components, and also some methods for situations where there is asymptotic independence between the variables. However, when different subsets of the variables have asymptotically different dependence structures, there are currently no methods that are applicable. The idea of my PhD project is to develop methods that can be used in these situations.