In environmental settings, extreme events can have devastating impacts, with examples including heatwaves and floods. In a changing climate, there is an increasing need to understand these events and reduce their effect. To prepare adequately for future extreme events it can be useful to carry out statistical analyses based on past observations. However, difficulties arise since interest may lie with events so extreme that they have not been previously observed. This means there may be an intrinsically limited amount of data available about past extreme events, which we can use to make inference about future ones.
Extreme Value Analysis provides theoretically-justified models that can be used in this context. Such methods allow us to make predictions involving extrapolation beyond the range of values previously observed. A wide range of statistical tools are available, including univariate, multivariate, and spatial techniques. The approach that is most appropriate to apply depends on the context of the problem being studied.
The reliability of any statistical inference depend on the quality of the data, which is negatively impacted through missing values. When modelling extreme events, where the amount of data is already limited, the effect of missing data on the analysis could be severe. An acute example is where the largest values of the process are always missing from the data; if a bad storm causes a river flow gauge to break, data about the corresponding extreme event will be lost; such information should also be considered in any statistical inference.
This project will investigate the effect of missing data on analysis methods for extreme values. We will develop appropriate inferential procedures that incorporate information about the underlying missing data processes. There is flexibility in the environmental applications, but would initially consider UK air pollution data from Defra, which previous analysis has revealed to have missing data issues.