Listed on this page are current research projects being offered for the Vacation Scholarship Program.
For more information on this research group see: Statistics
Applying and Interpreting Topological Data Analysis
Topological data analysis (TDA) is a technique incorporating algebraic topology to gain greater insight from large data sets. This project will explore applying TDA, generating graphical representations to explore and understand the relationships identified, interpreting the analysis, and communicating results. Requires knowledge of some statistical software (R preferred, python also suitable).
Contact: Paul Fijn paul.fijn@unimelb.edu.au and TriThang Tran trithang.tran@unimelb.edu.au
Projects in Generative Models Learning from Imprecisely Measured Data
Most statistical methods are designed for perfectly observed data, while lots of real data is measured with errors. For example, the ANHS and the U.S. NHANES surveys rely heavily on participants’ self-reported behaviours, such as what they ate in the last 24 hours. Studies have shown that this type of data can contain up to 75% noise. To illustrate, let X represent a participant’s true food intake. However, what they actually report is W = X + E, where E is an unknown random error. In some cases, the error E can be so significant that it accounts for as much as 75% of the total variability in the reported value W across the population. Analysing such data "as is" can lead to incorrect conclusions, which can negatively affect health policies and treatment guidelines. The project aims to solve this problem by developing a new generative model-based method that is theoretically justified and robust to handle large, complex datasets contaminated by measurement errors. Students are expected to learn the problem, related literature and methods, run some simulation experiments, and help develop R or Python packages under supervision.
Contact: Wei Huang wei.huang@unimelb.edu.au