Statistical breakthroughs can help scientists calculate the worst-case probability
Of all things, the most likely to end life on Earth as we know it: meteorite impact, Extreme climate change, Pandemic, solar flare?
A new statistical method can help scientists more accurately analyze the worst (or best) situation by combing through information about rare but very important events. This method can help everyone from investors to government officials and insurance companies make informed decisions about the potential dangers of scarcity of data.
The mathematical biologist said: “Although they are rare by definition, they do happen, and they are important.” Joel Cohen, The co-author of the study. “We hope this is a set of useful tools to better understand and calculate these risks.” Cohen is a professor at Rockefeller University and Columbia University’s Earth Institute, and is currently a visiting scholar at the University of Chicago.This survey Just published inside Proceedings of the National Academy of Sciences.
A new study looks at a statistical method used to calculate the probability of extremely rare but catastrophic events, such as meteorite impacts believed to have caused the extinction of dinosaurs. This is a tourist station near the Petrified Forest National Park in Arizona. (Kevin Krajic/Earth Institute)
Statistics is a science that uses limited data to understand the world. Its questions include “When is the best time to spray pesticides on crops?” “How likely is it that a global pandemic will shut down a lot of public life?” For a century, the statistical theory of rare but extreme events has been a relative In newer fields, scientists are still cataloging the best ways to handle different types of data. Calculation methods can significantly influence conclusions, so researchers must carefully adjust their methods of data.
Two powerful tools in statistics are mean and variance. Most people are familiar with the average: if a student scores 80 points on the exam and another student scores 82 points, then their average score is 81. On the other hand, variance measures the range of distribution of these scores. If one student scores 62 points and another student scores 100 points, you will get the same average of 81 points, but the classroom impact will be very different.
In most cases, the mean and variance are finite numbers. But when you see extremely rare catastrophic events, things become strange. In most years, there will not be a huge explosion of activity on the surface of the sun large enough to blow up all the electronic equipment on the earth-but it is very likely to happen once, if it happens this year, the result will be catastrophic. Similarly, the vast majority of startups have failed, but occasionally Google or Facebook will appear.
“There is a class of large events that rarely happen, but they are usually enough to push the mean and/or variance to infinity,” Cohen said.
These situations require their own special tools. Understanding their risk (called “heavy-tail distribution” events in statistics) is important to many people. Government officials need to know how much energy and money they can reasonably invest in disaster preparedness; investors want to know how to maximize returns while also considering extremely unlikely situations.
Cohen and his colleagues studied recent mathematical models used to calculate risk. The model divides the variance in the middle and calculates the variance above and below the average. This aims to provide more information about downside and upside risks. For example, it may be found that a new technology company is much more likely to fail (that is, below average) than to succeed (eventually above average). This is what potential investors might want to know. However, this method has not yet examined the distribution of low-probability, very high-impact events with infinite mean and variance.
Running the test, the scientists discovered that the standard method of processing these numbers, called semivariance, does not produce much information. But they found other ways.For example, they can calculate Logarithm of the mean To the logarithm of the semivariance. “Without logs, you will get less useful information,” Cohen said. “But for logs, the restricted behavior of large data samples provides you with information about the shape of the underlying distribution, which is very useful.”
“We think that financial mathematics, agricultural economics and even epidemics have practical applications. But because it is so new, we are not even sure what the most useful areas might be,” Cohen said. “We just opened this world.”
The researchers did not claim to fully know what is most likely to end life on Earth.
The other authors of the study are Mark Brown of Columbia University; Chuan-Fa Tang of the University of Texas at Dallas; and Ren Shangzhi of the Chinese University of Hong Kong.
Adapted from a press release from the University of Chicago.
