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How much is enough? That depends on the subject.

When John D. Rockefeller, the world’s first billionaire, was asked, “How much is enough?” he famously answered, “Just a little bit more.” When it comes to sampling and statistics, the answer usually involves what Rockefeller was well known for — money.

“Collecting data can be very expensive,” said assistant professor Felix Gnettner, who just planted his roots in the Department of Mathematics and Statistics at Ģ����ý in January. He arrived after completing one year of postdoctoral work at Colorado State University.

“You don’t want to collect too much data. For example, in medical trials you don’t want to contact 100,000 people if the process is exhausting. If you’re testing manufactured goods, you don’t want to test too many of them because it would waste money. That thinking can be applied to anything where you just take samples,” Gnettner said.

Monte Carlo algorithms

This has nothing to do with predicting how you will do at the gambling tables. Rather, it is a mathematical tool to approximate unknown values with simple averages using large sampling sizes.

“When do you have enough data? When have you or the machine learned enough to qualify your data? Do I have to continue taking a sample? I might make a mistake if I don’t have enough data.” Those are questions statisticians and the users of their products repeatedly ask.

Gnettner is performing theoretical research to determine stopping criteria for Monte Carlo algorithms.
“You continue sampling until you get statistical evidence that the unknown value of interest is located in one of a few pre-specified intervals. In some cases, you decide for a wrong interval by chance. Nevertheless, you are always in charge of the tolerance probability that this happens.”

Other research areas

Two other areas Gnettner researches are anomaly detection and methods to analyze high-dimensional and functional data.

Anomaly detection can be used in many fields, including temperature curves or gene expression. For example, ocean temperature curves that deviate in location or shape from the norm can be indicators of El Niño. Anomalies in genomic data can be an indicator of a disease. 

To what extent can that gene expression deviate before it is a risk indicator? 

While a mathematician is neither a medical doctor nor an oceanologist, he can operate on large data sets, separating what is “deep,” or well within the statistical profile, and what is well outside of the norm. Armed with that knowledge, medical researchers can then make their evaluations. The data crunchers parse the routine from the unexpected.

Gnettner said that is accomplished by depth functions that measure how deep an object is located within a sample. These functions can be also approximates by Monte Carlo methods. 

“My part of research is to guarantee that this work is reliable,” Gnettner said. “There are many different types of anomalies and not all of them can be detected by any method. I want to understand and quantify the strengths and weaknesses of such methods.”

His other area of research is related — analyzing statistical methods for high-dimensional and functional data to prove that they do what they are supposed to do.

“Often, researchers are interested in the gain in accuracy if the amount of available data grows, and in potential losses in accuracy if the dimensionality grows.”.

Vast differences in educational systems

Gnettner, 31, said he has always been a numbers person, but it wasn’t until he was doing his postdoctoral work that he decided to go into academia.

“I enjoy the academic freedom. You can choose the projects you’re working on. You’re not entirely tied to profit goals. You can choose the people you are working with in your research,” the German native said.

His bachelor’s, master’s and doctoral degrees all came from Otto von Guericke University, Magdeburg, Germany, in 2018, 2019 and 2024, respectively. He also attended a STEM-focused high school. “As a child, it’s been easier for me to deal with numbers than to learn writing,” Gnettner said.

He said he was drawn to SDSU because of “an attractive offer and a very positive impression during the job interview.” He is looking forward to collaborations with colleagues in his department.

In addition to working on his research projects, Gnettner also is teaching undergraduate statistics for engineers and will teach graduate courses in the fall. “I’m quite happy with my students. They’re committed. They’re willing to work, and that’s nice.”

He notes there is a vast difference between the higher education systems in the United States and Germany.

“SDSU classes are more structured with multiple exams in a term. In Germany, there is usually one final per class and that’s it. Thus, the teaching style here is more focused on interaction with students. In Germany, there are no tuition or fees. This gives more people access to higher education, but it reduces some students’ commitment.”

Among Gnettner’s outside interests are climbing and bouldering. For that, he has joined a climbing gym in Sioux Falls.

“With climbing, you have to focus. You can’t think about math. That is why I like it. It helps me to mentally relax.”