To help propagandize the usefulness of statistics for the regular public, I would like to dedicate some time every week to telling the stories of various people who made large impacts on our everyday lives through the use of statistics. I believe that common knowledge of these methods could enrich or empower citizens to be more active in their communities and also reason more rationally about the notion of risk. This post is going to be about E.J. Gumbel, who was an important figure in the formation of statistics.
Elias Julius (E.J.) Gumbel began his career as a mathematical statistician shortly before World War I. Statistics at that time was roughly 20 years old and was still taking hold of the scientific community. During the Weimar era, many political, industrial and judicial figures were in the pocket of the nazi party, which at this point was still pretty much just a violent street gang that marauded the homes of political opposition and minorities. The old-guard was angry at the amount of power and prestige they had lost after the kaizer was removed, and thus wanted to use the militaristic, right wing doctrines of the nazis for their own gain.
E.J. Gumbel witnessed the cold-blooded murder of a close friend by a gang of nazis in broad daylight and attended a trial in which the judge did not even consider any evidence against the brownshirts who committed the murder and set them free. In response to this Gumbel used his skills as a statistician to begin an investigation into the wider judicial system and the political murders of the nazis, which led to the publication of Four Years of Political Murder in 1922. After releasing more anti-nazi publications and evidence, he quickly became one of the most hated german intellectuals among the nazi party and their sympathizers.
Bookshops would refuse to put Gumbel’s books on their shelves for fear of being targeted by the brownshirts. Gumbel was finally forced out of his university by nazi sympathizers in 1932 and went on to teach in France and then in the United States. It was in the United States where he would embark on furthering a vital and underappreciated topic in statistics: extreme value theory.
The Problem of Floods
The origin of extreme value theory comes from the study of floods. Flood control is interested in protection against inundations. An inundation happens when water flows where it shouldn’t. Consider a water station along a river that computes the mean daily discharge through a given area, measured in cubic feet per second. Out of the 365 days of measurement per year, the day with the greatest discharge is called the annual flood (and it may occur across multiple days as well). Every waterway has an annual flood, but these floods need not lead to inundations, which is what people really care about. The purely empirical hydrological analyses of the engineers simply didn’t work well because the engineers of the time didn’t realize that they shouldn’t be analyzing the discharges themselves, but instead the distribution of discharges. We need to scientifically model what could happen and measure that risk, not what has already happened. The historical data is simply used as a means to determine the character of the distribution and the relevant statistics. However big floods get, there will always be a bigger one coming. Engineers need to be able to think about the flood situation decades in advance.
E.J. Gumbel derived what is now known as the Gumbel Distribution, which is a cornerstone of flood frequency analysis that helps us better model the maxima and minima of a number of samples from many distributions.
Here is a basic introduction to flood frequency analysis to explain the core concepts.
Here is an approachable Microsoft Excel tutorial on flood frequency analysis using the Gumbel distribution for those who are curious to learn more.
Extreme value theory can be applied across any discipline you can imagine in several use cases, so it is worth checking to see if you yourself can apply this idea to an extreme value problem in your own life.