5 minute read
Man of extremes
From the fastest sports records to maximum insurance coverage: John Einmahl focuses on extreme values. In doing so, he himself combines two extremes, namely fundamental mathematics and practice-based research.
By Yannick Fritschy
What is the highest we can achieve? What is the worst thing that can happen to us? We want to know what the extreme possibilities are in all kinds of situations. But these boundaries are not always easy to define.
Professor John Einmahl specializes in research into extreme values. This is a branch of mathematical statistics, an applied area of mathematics. “Actually, I focus on fundamental math. 80 to 90 percent of the time I’m proving theorems to understand how something works,” he says.
At the Faculty of Economics, Einmahl’s work is, therefore, classed as highly theoretical. But for mathematicians, it is very practical. Because research into extreme values has many applications, from the world record for the 100-meter sprint to insurance damage in the event of a largescale catastrophe.
BRAM BELLONI
Fastest Faster, higher, stronger. Following the Olympic motto, athletes continually set new, unfathomable records. Only last year, Kenyan Eliud Kipchoge was the first human to run a marathon in less than two hours. Where does it end? Together with Tilburg colleague Jan Magnus, Einmahl predicted extreme records for the 100 meters and the marathon in 2006. For the 100 meters, they calculated 9.36 seconds as the ultimate top time. A time that was considered impossible fifteen years ago, when the world record was at 9.79 seconds. But when Usain Bolt ran the 100 meters in 9.58 seconds in 2009, the statisticians’ prediction suddenly turned out to be realistic.
On the other hand, the marathon was a lot harder to predict. In 2006, Einmahl and Magnus decided that the world record would remain just over two hours and two minutes in the next few years. Now the world record is 2:01.39 – and even under two hours if you include the time set by Kipchoge, who did not run an official race. “In our prediction, we assumed that the average quality of the top runners would remain the same over the years. That seems to have been the case with the 100 meters in recent years, but not with the marathon,” explains Einmahl. “In addition, for marathons you have to take into account changing circumstances, such as the course and whether the runners run in groups or alone.”
But why do statisticians focus on predicting sports records? “It’s less important to society than research into insurance benefits, for example, but it’s something that attracts a lot of people,” says Einmahl. “Our research was published in leading journals and received a lot of attention in international media.”
Oldest If you look at a graph of life expectancy at birth in the Netherlands, you see a clear increase from 71.4 years in 1950 to 81.8 years in 2018. So, on average, we are living longer and longer. You would, therefore, expect that the maximum age a human can reach would also shift further and further. But that does not seem to be the case.
In 2017, Einmahl, together with his son Jesson and Laurens de Haan, applied the theory of extremes to our maximum lifespan. It turned out that we have been hitting a wall since 1986, and that wall is set at approximately 115 years. There is a margin of error, you could reach 120, but it seems that no one can reach 200.
“Some researchers claim that there is no maximum age. Our research shows that there is,” says Einmahl. “This is a very strong point of extreme value theory: you can determine whether there is a limit to something. In other statistical research, you have to choose in advance whether to use a model with or without a limit.”
How can the average age increase, but not the maximum age? “In the past, people more frequently died at a young age,” says Einmahl. “But I don’t know why you can’t live to be 200. I’m not a biologist.”
Most disastrous A dike must be high enough to withstand the strongest storms. But how high is high enough? You can make the dike tens of meters high just to be sure, but that costs a lot of money and is bad for the view. It would be better to have a dike that is just high enough to (almost) never flood. In the Netherlands, it has been established that a flood like the one in 1953 may only occur once every 10,000 years. With extreme value theory, you can calculate which dike height corresponds to this.
Similar research is carried out into the maximum strength of an earthquake, for example in Groningen. Based on this, you can determine what type of foundations the houses in the area should have.
Another important field of application of extreme value theory stems from this. Suppose a catastrophe were to occur, how much money would an insurance company have to pay out? An insurer wants to have sufficient reserves not to go bankrupt in such a case. But, on the other hand, they do not want to require premiums that are too high, because then customers will switch to the competitor.
The maximum payment in the event of a calamity is a lot more difficult to calculate than sports records or maximum life expectancy. “In the 100-meter sprint, Usain Bolt only goes a few percent faster than the number one hundred. And the oldest person is only a few percent older than the hundredth on the list of oldest people,” says Einmahl. In the case of the largest catastrophe imaginable, the amount of the damage is no less than twenty times higher than in the number forty on the list of largest disasters. As a result, the total payout is very difficult to predict, which makes the research a lot more exciting. We can’t perform miracles, but we use the best methods to predict these things in the best possible way.”
