Research for Undergraduates

A number of faculty members within the Statistics Department are available to provide research opportunities for undergraduate students. It is expected that most of these opportunities will be for students who are working towards Honors in the Major (in Statistics).

The faculty members listed below have directly expressed interest in working with undergraduate students and have provided information about the type of opportunities that could be available. It is possible that other faculty members in the Department might also be available under certain circumstances.

It should not be expected that any given faculty member listed below will automatically agree to every request for undergraduate research. Their willingness to participate will depend on how many other undergraduates are already working with them and other time constraints that they may have. Also, as noted, the highest priority will generally be given to those students working towards Honors in the Major.

Students working towards Honors in the Major need to be aware of the College and Department regulations regarding Honors. In particular, students are required to register for Stat 681 and Stat 682 while working on their research. Note that, as part of Stat 681 and Stat 682, there will be some “group” sessions each semester to discuss topics of common interest (e.g. strategies for presentation, ethics, reference sources).

Assuming that you will be doing your Honors research during the Fall and Spring of your senior year (which is recommended), usually the best time to approach a professor is during the semester before you intend to perform the research. In some circumstances you can make contact earlier than that. However, the stronger your training is in statistics, mathematics, and computer science, the more prepared you will be for a productive research experience.

Below is information provided by each of the faculty/staff members who expressed direct interest and also an email address for contact. If you have any general questions about research opportunities, feel free to contact Derek Bean (bean3 at wisc . edu).

Cecile Ane

My research focuses on statistical methods to answer questions in evolutionary biology. For most of what we do in my group, we use evolutionary trees, now inferred from very large molecular sequence data sets. We use and develop methods to answer questions about the molecular process of evolution, evolution of morphological traits, detection of natural selection, species delimitation, etc.

1. What projects are suitable for undergraduate students?
I anticipate that most such projects will be part of larger collaborative projects.

2. What are the required skills for undergraduate students to work on these projects?
Calculus, introduction to mathematical statistics, basic applied statistics, programming in R, Julia or another computing language. An interest in biology and basic knowledge of genetics would help.

3. What will students learn from their research experience?
Students will gain experience with statistical methods applied to problems of evolutionary biology and their application to real world problems.

Karl Broman

My research concerns on statistical problems in genetics and genomics, with a particular focus on mapping genetic loci contributing to complex diseases in model organisms (such as mice). My work has three parts: data analysis, development of improved statistical methods for analyzing data, and implementation of such methods in computer software. I also have a strong interest in data visualization.

1. What projects are suitable for undergraduate students?
Projects have included the analysis of mouse experiments aimed to identify genes contributing to various diseases, including diabetes and cancer.

2. What are the required skills for undergraduate students to work on these projects?
Introductory statistics, linear regression, basic R programming, and some genetics and biology.

3. What will students learn from their research experience?
Students will develop an understanding of how statistics is applied in practice and will improve their skills in programming and data analysis.

Christina Kendziorski

My work is focused on developing, evaluating, and implementing statistical methods for analysis of large datasets collected in studies that aim to identify the genomic basis underlying complex diseases such as cancer and diabetes. I have an active research group that meets weekly to present progress and discuss new ideas. Although most of my work involves graduate students and postdocs, I have worked with many undergraduates over the years. Each of the students focused on a statistical problem that arose in one of the laboratories of my collaborators.

1. What projects are suitable for undergraduate students?
Specific research projects have included: designing more efficient and effective (meaning cheaper and more informative) experiments; identifying genes that predispose a person to cancer using dense genotype data (1 million genotypes per person); identifying networks of genes that change across interesting biological conditions (e.g. cancer vs. healthy, pre-diabetic vs. diabetic); extending methods for next-generation sequencing studies from two-group comparisons to time course experiments.

2. What are the required skills for undergraduate students to work on these projects?
Calculus, introduction to math stat, basic regression analysis, basic programming in R; and the more genetics and biology a student knows, the better!

3. What will students learn from their research experience?
I expect they have learned a bit about some problems in statistical genetics and genomics, and have gained some insight into what graduate student life is like. All of the undergraduates I've mentored present their work in our group meetings, and eventually at a conference or symposium. Consequently, they learn about effectively summarizing scientific results and giving presentations.

Bret Larget

My research interests include statistical methods applied to biology in general and phylogenetics, the reconstruction of the evolutionary past from DNA sequences and other molecular data available in organisms today.

1. What projects are suitable for undergraduate students?
A good undergraduate project is part of a larger collaborative science project, but has a defined and narrow scope and can be completed in one or two semesters. A current student is working on comparing two methods to simulate realizations from a continuous-time Markov chain conditioned on both endpoints. Such models are used in likelihood-based approaches to studying molecular evolution.

2. What are the required skills for undergraduate students to work on these projects?
I'd like a student to have completed Stat 309 and another stat course. I expect the basics of linear algebra for many projects. Basic understanding of biology and genetics is useful. The more programming background the better. R can work, but many of my projects are best done in C++. Maybe the student can teach me something better!

3. What will students learn from their research experience?
A past undergraduate research student of mine got her PhD in Computer Science at UC Berkeley and now works for Pixar. A student should get a taste of what graduate research may be like.

Rick Nordheim

My current research interests include applications to various problems posed by researchers in the social sciences. I am also interested in research questions brought up in my teaching. Some of these include issues like robustness of various methods of inference in regression if some of the assumptions are not met or comparisons of various sampling strategies depending on the distributions of values of survey data by strata, cluster, etc.

1. What projects are suitable for undergraduate students?
I anticipate that most projects will fall under the second (motivated by teaching) category. (Participation in a collaborative research project with social scientists is also possible depending on the nature of the project and the background of the student.)

2. What are the required skills for undergraduate students to work on these projects?
Completion of a course in regression analysis (Stat 333) and a good background with R (Stat 327 --- preferably including the intermediate module). For problems related to survey sampling, Stat 411.

3. What will students learn from their research experience?
Students will gain experience with providing solution to practical applied problems. I will also place emphasis on communicating results (primarily in written form --- but also, perhaps, orally) since this is an important part of a statistician’s career.

Peter Qian

My research interests include modeling massive data, complex system simulation, uncertainty quantification, design of experiments, the interface between statistics and optimization, statistical methods for information technology (nanotechnology, energy, and other high-tech industries), and experimental design for machine learning and data mining. Recently, I have developed an interest in designs motivated by Sudoku. I have worked with several undergraduates in the recent past. All of the research problems have been well-defined and are self-contained.

1. What projects are suitable for undergraduate students?
One student focused on constructing subset Latin hypercube designs. Another student constructed asymmetric nested lattice samples. The topic of another student focused on constructing Samurai Sudoku based designs. (These are among the class of designs motivated by Sudoku.) Another student used experimental design ideas for efficient cross-validation in machine learning. Future projects would be of the scope of these examples.

2. What are the required skills for undergraduate students to work on these projects?
Besides an understanding of introduction to math stat and basic regression analysis, I require the students to have some basic background in statistical programming at the level of defining new functions and constructing small loops. Either R or Matlab will work fine. For the statistics background, the student should have completed Stat 310 and 333. Stat 424 is highly recommended (but not absolutely required).

3. What will students learn from their research experience?
They have all enjoyed the experience. Some of them said that their research experience motivated them to pursue an advanced degree in statistics or a related field. Some of these students have presented their work at the UW-Madison Annual Undergraduate Symposium and received positive feedback. In addition, some of their projects have led to journal publication. I believe that the students' research experiences add significant value to their applications to graduate school. For example, a professor at UC-Berkeley was particularly impressed by the research experience of one of my undergraduates and contacted me for more information when considering this student for an RA position.

Karl Rohe

My research aims to provide tools to better understand networks (social, biological, communication, etc). There are *typically* three parts to the research; (a) motivation, this comes from a dialogue with domain experts; (b) fast algorithms, because we are in the age of big data, algorithms must be fast; and (c) statistical inference, because there is usually a bigger questions than "what does my data contain." Instead, the question is "what does the population or data generating mechanism look like."

1. What projects are suitable for undergraduate students?
Algorithmic development and implementation and/or data analysis.

2. What are the required skills for undergraduate students to work on these projects?
Dedication, linear regression, basic R programming, a comfort with mathematical notation.

3. What will students learn from their research experience?
Students will be better prepared to take the first steps towards understanding "big" data.

Sijian Wang

My research interests include high-dimensional data analysis, variable selection and model selection, statistical learning and machine learning, longitudinal data analysis, survival data analysis and statistical modeling in medical sciences. I also have rich collaborations with doctors in medical school. Two main areas I am focusing on are orthopedics & rehabilitation and anesthesiology.

1. What projects are suitable for undergraduate students?
There are three types of potential research projects:
  1. Propose some simple but novel statistical methods for high-dimensional data analysis. It can be a simple or straightforward extension of the existing methods.
  2. Apply some existing statistical methods to some complicated and real scientific problem motivated datasets.
  3. Work on a real project collaborated with doctors in medical school. This project can be the data analysis or design of experiment.

2. What are the required skills for undergraduate students to work on these projects?
Calculus, Linear algebra, Regression analysis, Programming in R/Matlab.

3. What will students learn from their research experience?
The first thing I expect the students have learned is to conduct the independent study/research, for example, reading research papers to understand some concepts and methods, which are not covered in class. I also expect them to have gained some basic experience of research, such as conducting simulation studies, conducting data analysis for a real problem, summarizing and explaining analysis results and communicating with people.

Zhengjun Zhang

My research areas are very diverse. On the application side: I have been conducting research on financial time series, time series forecasting, asset pricing and portfolio management, graphical models, clinical trials and medical statistics, computer simulation, optimization, climate models, etc. On the methodology side: I have been studying nonlinear multivariate analysis, nonlinear dependence measures, and nonlinear time series etc. On the theory side: I have been focusing on max-stable process and related topics.

1. What projects are suitable for undergraduate students?
  1. Studying the nonlinear dependence measures (the quotient correlation coefficients (QCC), the generalized measures of correlation (GMC)) introduced in my earlier work and applying them to some real problems such as identifying important genes in predicting patients' health status.
  2. Studying several nonlinear time series models introduced in my earlier work and applying them to financial time series data and weather time series data.
  3. Studying portfolio management using my extreme co-movement models.
  4. Studying independent component analysis and simulating max-independent component analysis.
  5. Studying and simulating the sufficient important difference (SID) and comparing it with the minimum important difference (MID) in clinical trials.

2. What are the required skills for undergraduate students to work on these projects?
  1. Requires Stat 310 and part of Stat 456.
  2. Requires Stat 309, 310, and 349.
  3. Requires Stat 310, 349 and some knowledge in finance.
  4. Requires Stat 456.
  5. Requires Stat 310.

3. What will students learn from their research experience?
In the recent two years, I supervised three honor theses (two from UW, one UW visiting student from China). All these three students were admitted to three of the best business, economic and financial engineering graduate programs in US. I taught them some basic skills such as: understanding the problems and the models, doing data analysis, writing programs, running simulations, drawing conclusions, and writing reports.

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