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Arts and culture 24 Jan 2017

The two statisticians that revolutionized the analysis of data recognized with the Frontiers of Knowledge award

David Cox and Bradley Efron’s work has proven indispensable for medicine, astrophysics, genomics or any field of knowledge that depends on data analysis. The discovery of the Higgs boson or cancer and AIDS research efforts owe a lot to the two mathematicians honored by the BBVA Foundation.

David Cox and Bradley Efron have been recognized with the BBVA Foundation Frontiers of Knowledge award in the Basic Sciences category for the development of “pioneering and hugely influential” statistical methods.

Cox and Efron’s techniques are used on a daily basis in the practice of statistical science, and have made an enormous impact in all the sciences which rely on the analysis of data,” in the words of the jury’s citation. For mathematician Trevor Hastie, professor at Stanford University and member of the jury, “they are the two most influential statisticians alive today, and true revolutionaries in their field.”

Cox’s contribution, known in honor of its creator as “the Cox regression,” is a powerful tool to explain the duration of a time interval between two events of interest, which depends on identifiable factors rather than mere chance. For instance, the mortality of a group of individuals due to a particular disease or a risk factor like environmental pollution.

The jury illustrates the technique’s application in the medical field by citing the conclusion that even a year of smoking cessation contributes to reduce mortality.

David Cox, professor at Oxford University, declared himself “enormously surprised and gratified” by the sheer range of scientific problems his method has helped address, and stressed its application in the medical field: “It is used in the study of cancer patients… there are many factors at work in an individual’s survival, including their social background, sex and age… which are the most relevant?”

This is the kind of issue that can be broached with his technique, published in 1972 in what is now the second most cited statistics paper in modern scientific literature.

The best secondary actor in statistics

Bradley Efron, professor of statistics at Stanford University, has invented a method, the bootstrap method, to estimate the margin of error of a given outcome; a must-know in science without which results are worthless.

The name bootstrap comes from the 18th century tales of Baron von Munchhausen, a favorite of Efron’s, and refers to the mechanics of the technique. In one of the stories, the Baron is drowning in a lake and saves himself by “pulling himself up by the strap of his boots,” explains Efron. The technique involves randomly resampling the data from the study sample time and time again, so it is these same data, with no additional inputs, that provide the margin of error.

In any analysis, the main role goes to the algorithm, whose job is to answer the question that the researcher is posing. The support role consists of determining how accurate that answer is, explains Efron. “So the bootstrap may almost never be the star, but it has become the best secondary actor in statistics.”

Efron admits that statistic’s role in science is “less fun” than the research that throws up the data to be analyzed, but is also clear about its importance “Scientists collect data, we analyze them. For instance, in the search for the Higgs boson what you do is gather a bucketful of data which ultimately boils down to a bump in the chart. But, how can we be sure that the bump is real and not a statistical artifact? (a factor that interferes in the correct interpretation of the result)? The bootstrap tells you.”

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