## Current RTG Projects

### PROJECTS (2015-16)

There are five RTG undergraduate research projects that will be conducted in 2015-16.

**Project 1:** Applied Functional Data Analysis (H.-G. Müller)

In this project the participating student will obtain data that contain functions (time courses) or can be viewed as being generated by underlying functions and will study, apply and compare various linear and nonlinear dimension reduction methods, including functional principal component analysis.

Prerequisites: Fluency with R, STA 135 or STA 141

**Project 2:** Quantifying Patterns of Survival and Reproduction for Cohorts of Flies (H.-G. Müller)

This project touches upon biodemography, ecology and evolution, functional data analysis, and survival analysis. There are several possible projects, including the study of a large sample of cohort lifetables for medflies. This project will be co-directed with Prof. Carey, Entomology.

Prerequisites: Matlab, R, STA 131B and STA 141

**Project 3:** Spatio-temporal covariance models for use in solar energy research (J. Patrick)

The amount of energy produced by a utility-scale solar energy plant is highly correlated with ground measurement of solar irradiance within the plant’s footprint. Thus, proper understanding and modeling of the irradiance data is of importance in both the planning and operation of the solar plant. In this project we will examine a number of ways to model the spatio-temporal covariance structure of the irradiance data. We will explore simple models in which isotropy (independence of spatial direction) and separability (the time and space covariance structures can be expressed as a product) are assumed. We will then explore more complicated models in which these assumptions are not made. We will use forecasting in time and spatial kriging as measures of how well the models perform. Pre-requisites include STA 131A and 141 or have experience programming in R. Preferably, the student will also have taken STA 137.

**Project 4:** Exploration of geometry of data in high dimensions and its effect on classification (W. Polonik)

High-dimensional data are rather the norm than the exception in our modern world. It is therefore important to understand how high-dimensional data, or a data cloud “looks like” in high dimension. To approach this challenge, we will read parts of the paper Hall, P., Marron, J.S. and Neemon, A. (2005): “Geometric representation of high dimension, low sample size data. “ Journal of the Royal Statistical Association, Series B, pages 427 – 444. This includes gaining familiarity with certain classification methodologies, such as Support Vector Machines. We will also attempt to reproduce some of the simulation studies presented in this paper.

Pre-requisites are (i) a certain level of understanding of probability theory, in particular familiarity with the law of large numbers and the central limit theorem usually taught in STA131A, and some experience with programming in R.

**Project 5: **Manifold learning with outliers (T. Lee)

An important problem in statistical and machine learning is the recovery of a possibility nonlinear low dimensional structure from noisy data collected from a high dimensional space. The true dimension of the structure is often unknown. The goal of this project is to investigate recovery methods when the measurements are not only corrupted by additive errors, but also with outliers.

Click here to see **ARCHIVE OF PREVIOUS RTG PROJECTS**