Extreme Events In Correlated Processes

History often turns on extreme events, be they man-made or natural. Examples are global financial crises, military strikes or radical political events, or natural disasters such as floods and earthquakes, in the latter. Extreme events are often associated with catastrophes, and the word ’extreme’ is sometimes substituted by ’freak’ to suggest something unnatural and undesirable, or ’rogue’ in the case of ocean waves. Generally, the economic and social consequences of extreme events are a matter of enormous concern.

When such catastrophes strike, it is easy to look back and analyze mistakes. But how do we gain a better understanding that can be applied towards the next event? It is often argued that extreme events are so implausible as to be negligible for planning purposes. Of course, extreme events are, by their definition, rare. However, what is rarer still is that a rare event never occurs at all. In particular, extreme events have a number of key characteristics that are found over and over again. We know that records must be broken in the future, so if a flood design is based on the worst case of the past, then we are still not prepared for possible floods in the future. Materials will fail due to fatigue, so if the body of an aircraft looks fine to the naked eye, it must still fail seemingly out of the blue if the aircraft has been in operation over an extended period of time.

Much of science has concentrated, until recently, on understanding the mean behaviour of physical, biological or social systems and their “normal” variability. Extreme events, due to their rarity, have been hard to study and even harder to predict. The science of extreme value statistics aims to describe the occurrence of extreme events in a general and unified way. Their application ranges from natural disaster insurance to global financial markets, from climate change mitigation strategies to tsunami warning systems, a universal advancement of theory for an abundance of technology-based innovations.

The long-term goals of this research are to develop new statistical and probabilistic models for extremes and to use them in a wide range of applied problems. In particular, we will develop a mathematical theory of extreme value statistics suitable for cases where individual events are correlated with each other over a wide range of spatial and/or temporal scales. Such complex behavior arises due to nonlinear interactions between the components of the system and has recently been established as a general and significant phenomenon. The emerging field of complexity science uses statistical analysis across such non-linear systems to find universal patterns and understand the behavior of these events over time. Prominent examples can be found in climatology, space physics, plasma physics and fusion research, communications traffic and socio-economic systems. Such a theory will allow us make contributions to hazard assessment — quantifying the worst case scenario — and the prediction of extreme events. It will also provide important guidance in developing strategies to cope with extreme events, minimize their impact and potentially influence their occurrence.