Research in probability and statistics

Probability and statistics provide a foundation for analyzing and making decisions about random phenomena in the real world. These research areas have a wide range of applications in social and natural sciences, engineering and business. With the rapid development of information technology, the field is becoming essential to innovations in computer science and data science.

Professors with interests in probability and statistics

• Xiaoli Kong
• Rohini Kumar
• Jose-Luis Menaldi
• Kazuhiko Shinki
• Tze-Chien Sun
• Yan Wang

Research areas

Probability theory

Research activities in this area include large deviations, homogenization of multi-scale diffusions and jump-diffusions and applications of probability and stochastic processes to mathematical finance.

Statistics

Research activities encompass both theoretical and applied aspects of statistics. Core areas include frequentist and Bayesian theory, multivariate and nonparametric analysis, time series analysis and various statistical modeling techniques. As the field expands, it increasingly intersects with data science and machine learning, leading to a broad impact on many applied disciplines.

Statistical machine learning

Research in this area mainly focuses on understanding modern machine-learning algorithms from a statistical perspective. We use fundamental mathematical principles of high-dimensional probability and statistics as our primary tool to explore the generalization error of learning algorithms for point prediction, develop distribution-free and provably valid prediction sets and provide insights into the underlying mechanisms of state-of-the-art algorithms like diffusion models and large language models.