EVT

Extreme Value Theory

Extreme value theory (EVT) is the mathematical underpinning for studying extreme events, and therefore risks, in the same way that probability theory more generally provides our mathematical understanding of uncertainty. Unfortunately, as of 2020, there are no courses at the University of Cambridge that teach EVT, and so students in this CDT will have to teach themselves and one-another using external resources.

Some takeaways from EVT are:

• You always need more data than you think.
  • Convergence under fat tails using the law of large numbers will probably take a long time.
  • Precaution is justified in such cases.
  • In a fat tailed distribution most observations are below the mean.
• Most data in a time series contains no information about risk.
• The world is not Gaussian and such approximations can be dangerous.

Resources:

• [Pop-Sci] The Black Swan: the impact of the highly improbable, NN Taleb
• [Youtube Video] https://www.youtube.com/watch?v=IiOSxaF5oxo
• [Free, intro maths, Fun comics] The statistical consequences of Fat Tails, NN Taleb
• [Expensive, short, engineery, lots of examples] An introduction to Statistical Modeling of Extreme Values, S Coles
• [High-faluted Maths, nice old book smell] The Asymptotic Theory of Extreme Order Statistics, Galambos

Precautionary principle for climate science, a risk perspective:

• https://necsi.edu/climate-models-and-precautionary-measures
• https://necsi.edu/necsi-work-on-catastrophes

Coronavirus:

• Nice paper on Pandemics from an EVT perspective, which claims the dubious honour of being so good that they managed to get wikipedia into their references in Nature Physics: https://www-nature-com.ezp.lib.cam.ac.uk/articles/s41567-020-0921-x
• https://arxiv.org/abs/2007.16096
• https://www.endcoronavirus.org/