Mentors and Project Descriptions


autumn 2025 Projects


Andrew Zhang: Functional Inequalities

Prerequisites: Undergraduate analysis and probability. Familiarity with abstract integration would be very helpful.
Project is best for: Junior (3rd year) or Senior (4th year and beyond)
Number of mentees: 2

If X is an n-dimensional random vector, it is natural to ask how real-valued functions of X concentrate around their expectation E[f(X)]. If X is uniformly distributed on a bounded open set with a smooth boundary, then classical results such as the Poincaré inequality provide a bound on the variance of f(X) that depends on the ambient dimension n. Remarkably, there are random variables which exhibit dimension free concentration properties such as a standard Gaussian vector through the Gaussian Poincaré inequality. In this DRP, we will do a guided reading of such functional inequalities, their relationship to Markov diffusions, and their implications for the theory of sampling.



Ethan Ancell and Kayla Irish: Multiple Testing

Prerequisites: Comfort with hypothesis testing and confidence intervals
Project is best for: Junior (3rd year) or Senior (4th year or beyond)
Number of mentees: 2

When an analyst considers multiple statistical inferences at once (for example, by conducting many hypothesis tests simultaneously), standard statistical guarantees such as bounds on type 1 error break down. The field of multiple testing addresses this problem by adjusting p-values as appropriate to yield bounds on metrics such as the family-wise error rate (FWER) or the false discovery rate (FDR). This DRP will have an emphasis on reading modern research papers from the field of multiple testing, with opportunities to code simulations as the mentees desire.



Hansen Zhang: Martingales and the Monkey Problem

Prerequisites: Basic probability at the level of STAT 311/394 or 390, and nice to have linear algebra (e.g., MATH 208) but not necessary
Project is best for: Sophomore (2nd year) or Junior (3rd year)
Number of mentees: 1

In this project, students will explore a famous probability puzzle: If a monkey types letters at random, how long will it take to produce the word “ABRACADABRA”? This deceptively simple question reveals rich mathematics. Students will model the problem using a Markov chain, where states track partial progress toward the target word, and compute the expected hitting time to the absorbing state. They will then connect the analysis to martingales, showing how fairness conditions and stopping times can provide alternative tools for reasoning about waiting times. The project emphasizes problem-solving, probabilistic modeling, and connections to real-world applications such as DNA sequence matching and information theory, which we may explore further given sufficient time.



Patrick Campbell: Introduction to Statistical Learning

Prerequisites: Stat 311 or equivalent required, coding experience in R/Python preferred, knowledge of linear algebra (i.e. Math 208) helpful but not required.
Project is best for: Sophomore (2nd year), Junior (3rd year), or Senior (4th year or beyond)
Number of mentees: 1

This project will explore the various methods and models relating to statistical learning, an evermore popular subject with various applications in medicine, business, and more. The reading project will explore various topics like linear/logistic regression, resampling methods, model selection, and more. We will mainly refer to the freely available textbooks “An Introduction to Statistical Learning with R/Python.” The mentee will explore and ultimately develop their own model(s) for an application/dataset of their interest. Prerequisites: Stat 311 or equivalent required, coding experience in R/Python preferred, knowledge of linear algebra (i.e. Math 208) helpful but not required.



Ronan Perry: Patterns, Predictions, and Actions

Prerequisites: The student should (i) have taken at least one course in probability and statistics (we will discuss concepts such as the normal distribution, likelihoods, expectations, conditional probability in 1 dimension) and (ii) be comfortable with computing in R or Python. The level of the DRP may be scaled to the level of the student and I will provide materials as necessary.
Project is best for: Junior (3rd year) or Senior (4th year or beyond)
Number of mentees: 1

This will be a guided reading of Patterns, Predictions, and Actions. We will study the problem of making predictions: evaluation of predictions, optimization of actions using observed data, generalization to unobserved data, and more. We will work through small problems and implement numeric solutions.



Rui Wang: Introduction to Causal Inference

Prerequisites: Standard calculus 1-3 sequence, introductory course in probability and statistics
Project is best for: Junior (3rd year) or Senior (4th year or beyond)
Number of mentees: 1

This project focuses on the fundamental concepts and methods of causal inference. The tentative content includes the potential outcome framework, causal graphical models, randomized trials, and observational studies. The specific content will be adjusted according to the mentee’s background and interests.



Yeting Wu: Analysis of Variance

Prerequisites: Completion of an introductory statistics course is required (e.g., STAT 311 or STAT 390) or equivalent background. It is suggested, but not required to. have prior exposure to R or Python for simple data analysis and visualization.
Project is best for: Any undergraduate
Number of mentees: 2

This project will explore how visual cues, such as profile photos, influence the formation of online friendships on social networking sites like Facebook. We will discuss theories from computer-mediated communication, including the hyperpersonal model and physical attractiveness stereotypes, and examine how statistical methods like factorial experimental design and ANOVA are used to study impression formation. The mentee will read and analyze research on online self-presentation, design choices in experiments, and how data are interpreted to draw social and behavioral insights.



Yuhan Qian: Introduction to Gaussian Processes

Prerequisites: STAT 394 highly recommended; STAT 341/342 recommended but not necessary
Project is best for: Junior (3rd year) or Senior (4th year or beyond)
Number of mentees: 1

Everyone knows about the Gaussian distribution. Its infinite-dimensional generalization, the Gaussian Process (GP), is also a commonly used tool in supervised machine learning, widely applied in regression and classification tasks. In this project, we will begin by exploring fundamental mathematical concepts and the standard GP model. We will also apply GP to solve some interesting problems in clinical trials.