Mentors and Project Descriptions
autumn 2026 Projects
Aditya Gantawar: Introduction to Applied Machine Learning
This project will begin with a brief survey of foundational and widely used methodologies in Machine Learning. The mentee will then choose a Machine Learning topic based on personal interest to study in depth together, followed by an applied project using that topic in an area of their own interest (e.g., sports, astronomy, neuroscience). Through this DRP, the mentee will gain exposure to a diverse range of ML concepts (regression, neural networks, clustering, etc.), develop a deeper understanding of their chosen topic, and gain experience modeling real data with machine learning.
Alan Boles: From linear regression to the Kalman filter (and beyond?)
Kalman filtering is a fundamental algorithm that provides estimates of unknown variables using a series of noisy measurements overtime. This algorithm is a workhorse in dynamic state estimation and has a plethora of applications. In fact, most humans probably interact with a system that uses (a version of) Kalman filtering everyday, but don’t even realize it (e.g. the GPS on your phone). Despite this, filtering and smoothing are topics rarely mentioned in the undergraduate statistics curriculum. These methods have a deep, yet accessible, connection to linear regression which we will explore in this project. We will work from a Bayesian perspective.
Andy Shin: Cell Count Analysis in Vaccine Trials
Vaccine clinical trials often evaluate efficacy by comparing the proportion of vaccine-activated memory B cells (MBCs) between groups. While standard binomial models are typically used, high biological variability leads to overdispersion. To address this, this project implements a Beta-Binomial model. Students will conduct simulation studies to compute statistical power and type-I error rates across various effect sizes and parameters.
No prior knowledge in biology or immunology is required. Project scope and readings are adaptable to the student’s background and interests.
Hansen Zhang: Geometry of Multivariate Statistics
An intuitive presentation of statistics is often passed over in favor of a rigorous, arithmetic treatment of its concepts. While univariate ideas are easy to grasp, their multivariate counterparts can quickly become difficult to grasp. What are degrees of freedom, really? How do you visualize correlation between several variables at once? What actually is multicollinearity?
It turns out there’s a unifying framework for all of this: the geometry of vectors — subspaces, projections, and angles. This directed reading project builds statistical intuition from the ground up using this geometric lens, working from simple regression through multiple regression and beyond. If you want to be able to see statistics rather than just compute it, this is the topic for you. Note: this topic is meant to be theoretical and fun, but NOT rigorous. We will mostly be drawing things, no proofs required!
Qinling Shi: Introduction to Time Series Analysis
This project will introduce the basic ideas of time series analysis and explore how statistical methods can be used to understand and forecast data collected over time. We will discuss topics such as trends, seasonality, autocorrelation, stationarity, and basic forecasting methods. We will also use R or Python to explore real-world time series datasets. Toward the end of the project, the student will have the opportunity to conduct a small analysis based on a dataset and topic of their interest.
Yanjiao Yang: Foundations of Time-to-event Analysis
Time-to-event analysis has been widely used in medicine, public health, engineering, economics, and many other fields to study how long it takes for an important event to occur. Examples include time to disease progression, treatment failure, equipment breakdown, or customer dropout. As events may not be observed for everyone during the study, familiar statistical methods are often no longer sufficient in this context.
In this DRP, we will study the core concepts of survival analysis in an intuitive and accessible way. We will learn how to describe and model time-to-event outcomes using tools such as Kaplan–Meier curves and the Cox proportional hazards model. There will be opportunities for hands-on data applications to connect statistical ideas to real-world questions. If time permits, we will also explore how survival analysis is related to broader topics in modern statistics, including missing data and causal inference. The goal is to give students a practical introduction to survival analysis and a glimpse of how these ideas appear in more advanced statistical research.
Yinqi (Billy) Zhao: Evaluating AI-Generated Summaries
AI systems can generate fluent summaries, but how should we evaluate whether those summaries are actually good? In this project, the student will study a public dataset containing machine-generated news summaries, human ratings, and automatic evaluation scores. We will learn how common metrics such as ROUGE and BERTScore work, then use visualization, correlation, bootstrap uncertainty intervals, and error analysis to ask when automatic metrics agree with people—and when they fail. The project will emphasize statistical thinking: choosing an appropriate analysis unit, quantifying uncertainty, avoiding misleading correlations, and explaining disagreements rather than chasing a single score. Depending on the student’s background and progress, we may also compare results across summarization systems or fit a simple predictive model. The final deliverables will be a reproducible notebook, a small set of clear figures, a short presentation, and a brief written report. No prior NLP or large-scale computing experience is required.
Yuhan Qian: Influence Functions and Statistical Sensitivity
How much can a single observation affect a statistical estimate? In this project, we will study this question through several related ideas, including leave-one-out methods, the jackknife, influence functions, and robustness. We will begin with familiar estimators such as the sample mean and linear regression, and investigate what happens when individual observations are removed, reweighted, or slightly perturbed. We will then use these examples to develop the idea of an influence function as a way to measure the sensitivity of a statistical procedure.
The project will combine mathematical derivations with simple simulations in R or Python, with an emphasis on developing intuition for why these methods work.