## Overview

Faculty in the department have active research programs that involve students during the academic year and summer. Summer research positions are open to Carleton students and are paid positions.

The faculty research projects for the summer of 2022 that have positions open for students are described below. Direct any questions you have about a project to the faculty running the project. The student stipend rate for the summer of 2022 is $500/week. A list of all science research opportunities and fellowships at Carleton College is also available.

If you would like to apply, please fill out out this application form by **midnight February 15, 2022**. You will be asked to list the project(s) of interest to you and provide an unofficial transcript. The number of students hired for each project is dependent on funding which is likely, but not certain, so the number of students ultimately hired for each project could change.

## Summer 2022 Project Descriptions

**Let’s write an R package! (Adam Loy)**

2 or 3 students (pending funding), June 13–August 5 (8 weeks)

Mode: in-person is preferred

Gauge R & R studies are used by engineers and physical scientists to assess the uncertainty associated with a measurement system. Understanding the uncertainty in a measurement system is important because this knowledge allows researchers to quantify the quality of the measurements they are receiving from a device. For example, Houf and Berman (1988) discuss a gauge R & R study to understand the variability of the instruments used to measure the thermal performance of semiconductor power modules. The study consisted of three randomly selected operators each making three measurements on ten randomly selected power modules. In this study, variability in the thermal measurements can be due to two sources: (1) the manufacturing process, and (2) the measurement instrument. The goal of this gauge R & R study was to determine whether the variability from the measurement instrument is small relative to the manufacturing process, as is desired in a quality measurement system.

In R, the qualityTools and SixSigma packages provide the primary means to fit gauge R&R models; however, neither package provides a complete modeling framework. The goal of this project is to create an R package that implements a (more) complete modeling framework for gauge R&R models in R, following the tidymodels philosophy.

During this summer project you will

- Learn about different estimation procedures for Gauge R&R models. Specifically, we’ll consider an ANOVA-based method as well as a Bayesian method.
- Think about how to visualize different sources of variability.
- Learn a lot about R programming and how R packages are constructed.
- Write a help files and a vignette (technical report) that will help users start using your R package.

Prerequisites: This project is open to students who have completed Stat 220 and Stat 250. Ideally, one student would have completed Stat 340.

**JAGS and Stan and greta, oh my! Navigating the opinionated waters of Bayesian computation (Adam Loy)**

1 student (pending funding), June 13–August 5 (8 weeks)

Mode: in-person or remote

Computation is a fundamental element of Bayesian statistics, allowing us to fit complex models where we can’t find closed-form solutions for the posterior distribution. While there is broad agreement about how fundamental computation is to the Bayesian paradigm in undergraduate statistics education (see Volume 28, Issue 3 of the Journal of Statistics and Data Science Education), it’s unclear what framework should be used in the classroom. In this project, we’ll review different ways MCMC can be implemented in R, comparing and contrasting the flexibility, extensibility, and required cognitive load. Specifically, we will compare how common Bayesian models can be fit using the following MCMC programs

- Just Another Gibbs Sampler (JAGS) via runjags and rjags
- Stan via rstan and brms
- greta
- NIMBLE

During this summer project you will:

- Implement a variety of Bayesian models using each MCMC program.
- Reflect on the usability, flexibility, and extensibility of each program.
- Write an article (and webpage) comparing these programs that statistics educators can use when deciding how to structure their Bayesian statistics course (including Stat 340 this fall!)

Prerequisites: This project is open to students who have completed Stat 220, but Stat 340 is strongly recommended so that the models make more sense.

**AMAAZEing mathematics: computational methods for studying broken bones (Rob Thompson)**

2-3 students (pending funding), 10 weeks (likely June 13 – August 19)

Mode: in-person is preferred

You are interning for the famous (fictional) archeologists Prof. Sydney Fox and Prof. Henry Jones, Jr., and you come upon a mysterious discovery…an ancient pile of broken animal bones deep in a cave. The professors want to know: who broke these bones? Was it an early human, smashing them with stone tools to get at the precious marrow, or bone crunching predators who long ago made their home in the cave? Or maybe one of the other interns stepped on them accidentally?

This story is more than fiction, of course. Archeologists often look for evidence in the remnants of the past — like old bones — to better our understanding of human activity. This evidence is growing increasingly quantitative, incorporating more sophisticated tools from applied mathematics, statistics, and computer science. For this project, we’ll help develop some of these new tools by joining a consortium of researchers known as AMAAZE. In particular, these researchers need better methods for understanding the stories that broken bones can tell: stories of early human and animal activity and interaction.

We will focus on the development and testing of methods in computational geometry for analyzing 3d scans of broken bones. Key tasks include the automated detection of the faces of the break, measurement of break angles, and methods for comparing break faces and reassembling fragmented bones. We will work with a data set consisting of 3d scans of elk bones, broken both by modern recreations of ancient human tools and by spotted hyenas (Scruffy and Nyota) from the Milwaukee zoo.

Minimal prerequisites are linear algebra, and some experience in computing (e.g. introductory computer science or statistics). During this project we will use some assortment of MATLAB, Python, and MeshLab for computing. Feel free to contact Rob Thompson to talk more about the project!