Statistics spotlight: Jonquil Liao, PhD student

Jonquil Liao
Jonquil Liao, PhD student in the Department of Statistics.

Jonquil Liao PhD x’26 never thought twice about coming to Madison from Hangzhou, China, where she began her undergraduate degree. With a long-held fascination for statistics, Liao was considering pursuing a graduate degree in the United States. 

Then, in 2019, an opportunity presented itself for Liao to transfer to UW-Madison in her third year of undergraduate studies, through the Visiting International Student Program (VISP). VISP allows international students to finish their undergraduate studies in Madison, with the final year of their bachelor’s also counting as the first year of the MS in Statistics and Data Science program.

When she first arrived in Madison, Liao said, “the thought of becoming a Ph.D. student didn’t even cross my mind.” But after diving deeper into research with Assistant Professor Joshua Cape, Liao found a specialization and never looked back. She is now in her third year of the PhD program in the Department of Statistics.

Exploring research interests

Early in her graduate studies, Liao specialized in financial statistics, but gradually became more enamored by statistical theory and what she called “well-defined problems.” Liao noted that in some newer applications of statistics, “there’s no solid theory that guarantees that your math always works,” making more well-grounded theories appealing in many cases.

At the same time, Cape inspired Liao to dig deeper into the foundations of statistics—the theories and methods that form the backbone of the discipline. Today, thanks to Cape’s mentorship, Liao said, “I can spend an entire day absorbed in the intricacies of a technical paper, relishing the experience.”

Assistant Professor Joshua Cape

Liao also credits Cape with sparking her interest in spectral clustering, a technique used to glean insights from large, complex datasets by identifying distinct clusters of points. The method has wide-ranging applications, including in computer science, biology, and the social sciences. Liao offered the example of LinkedIn to illustrate one way spectral clustering can be useful: “All of the users on LinkedIn form a huge network, and we can use spectral clustering to identify the communities in this network.”

In recent years, advances in machine learning have opened new possibilities for many statistical methods, including spectral clustering. Innovative work in this area, by researchers like Liao and Cape, will help integrate established theories and methods with powerful emerging technologies, potentially fostering new discoveries.

A ‘second home’

Beyond the classroom and the research lab, Liao has enjoyed roles as a teaching assistant for courses such as Applied Statistics and R for Statistics, as well as interacting with faculty and fellow graduate students. She described the department as “inclusive” and Madison as “a second home”.

Liao entered her PhD program eyeing an eventual position in industry, but she now sees a variety of appealing career paths ahead of her, including potentially in academia. Through collaborative work with faculty, she has developed research skills that will serve her well in any future role. And as the discipline of data science continues its explosive growth, opportunities abound for students like Liao to apply their statistical expertise across a seemingly unlimited range of fields.

Written by: Thomas Jilk, marketing & communications specialist

For more information about our PhD program options, visit the program webpage.