spring 2020 Projects

Anna Neufeld: Disease Modeling

Student: Rachael Ren

Slides | Writeup

Prerequisites: Knowledge of R will be useful!

We will start by reading introductory material on SIR compartmental models for disease modeling, and will work to implement these models in R. These are deterministic differential equation models whose output depends on knowledge of various input parameters. After becoming comfortable with the models, we will discuss how statisticians estimate the parameters of these models using current outbreak data in the face of uncertainty, and how the models are then used for predictions and forecasting. The project will evolve based on the interest of the student and relevant currnt events.

Shane Lubold: Random Graphs

Student: Gordon An

Slides | Writeup

Prerequisites: Some exposure to probability. Some exposure to, or an interest in, graph theory.

In this project, we will study random graph theory and how the behavior of these graphs change as the size of the graph grows. We will focus primarily on a simple graph model with a number of interesting properties, the Erdös-Rényi model. In this simple model, we generate a graph on n nodes, where each node connects to any other node with probability p(n), which can depend on the graph size n. We will use theory and simulations to derive key properties of this model, such as the distribution of the degree of a vertex or the number of cliques of any size. We will also explore other exciting properties of this model. For example, if the ratio p*n grows at a certain rate as n gets big, then the graph will, for example, exhibit large cliques with probability 1. The proof of these ideas uses only basic statistical ideas. We will prove the conditions that guarantee this behavior and use simulations to explore how large the graphs must be the see this behavior. This project will expose students to the exciting field of random graphs and will give them a good understanding of how simple statistical tools can answer complex questions.

Sheridan Grant: Causal Inference: DAGs and Potential Outcomes

Student: Grace Shen

Slides | Writeup

Prerequisites: Familiarity with linear regression and facility with Gaussian distributions (preferably multivariate)

This project will be reading-focused, rather than data analysis. It’s intended for a junior or senior student who is interested in learning about Causal Inference – a huge topic in graduate-level statistics and stats research–perhaps as a prelude to applying for PhDs. You’ll read classic papers and parts of textbooks on two approaches to causal inference, potential outcomes & graphs. For the final presentation, you’ll contrast the two approaches as applied to a problem (practical or theoretical) of your choice.