School of Mathematics & Statistics

Information about postgraduate research opportunities and how to apply can be found on the Postgraduate Research Study page. Below is a selection of projects that could be undertaken with our group.

Bayesian methods to detect nanoclustering in single molecule imaging experiments (PhD)

Supervisors: Mayetri Gupta
Relevant research groups: Modelling in Space and Time, Bayesian Modelling and Inference, Statistical Modelling for Biology, Genetics and *omics, Imaging, Image Processing and Image Analysis

Recent microscopic imaging technologies being developed now allow scientists to track and record the trajectories of individual molecules within living cells at nanometer scales over infinitesimal amounts of time. Discovering “nanoclusters” of such molecules - discrete areas within the cell (over space and/or time) which are important in terms of biological function - can give researchers an understanding into transient, functional states of cellular activity that underpin critical biological functions that may be taking place in the living organism. It can also establish how these correlate with changing experimental conditions, paving the way for future research into effective medical interventions. The high volume and density of individual molecular trajectory data, combined with the correlated and interacting trajectories of moving particles with state transitions over time, makes it challenging to accurately identify these nanoclusters over space (spatially) and over space and time (spatio-temporally), using standard statistical approaches. This project will aim to develop novel statistical visualization and clustering approaches for the detection of nanoclusters, making use of Bayesian hierarchical modelling techniques, latent variable modelling, and multi-directional block clustering methodologies, and compare and contrast the effectiveness of model-based and non-model-based clustering approaches in determining meaningful features within the data. The techniques developed can potentially be useful across fields ranging from medical genomics and imaging to diverse engineering and transportation applications.

Statistical detection of cellular communities in cancer progression (PhD)

Supervisors: Mayetri Gupta, Hien D. Nguyen (La Trobe University)
Relevant research groups: Bayesian Modelling and Inference, Computational Statistics, Statistical Modelling for Biology, Genetics and *omics, Biostatistics, Epidemiology and Health Applications

Recent microscopic imaging technologies being developed now allow scientists to track and record the trajectories of individual molecules within living cells at nanometer scales over infinitesimal amounts of time. Discovering “nanoclusters” of such molecules - discrete areas within the cell (over space and/or time) which are important in terms of biological function - can give researchers an understanding into transient, functional states of cellular activity that underpin critical biological functions that may be taking place in the living organism. It can also establish how these correlate with changing experimental conditions, paving the way for future research into effective medical interventions. The high volume and density of individual molecular trajectory data, combined with the correlated and interacting trajectories of moving particles with state transitions over time, makes it challenging to accurately.

Modality of mixtures of distributions (PhD)

Supervisors: Surajit Ray
Relevant research groups: Nonparametric and Semi-parametric Statistics, Applied Probability and Stochastic Processes, Statistical Modelling for Biology, Genetics and *omics, Biostatistics, Epidemiology and Health Applications

Finite mixtures provide a flexible and powerful tool for fitting univariate and multivariate distributions that cannot be captured by standard statistical distributions. In particular, multivariate mixtures have been widely used to perform modeling and cluster analysis of high-dimensional data in a wide range of applications. Modes of mixture densities have been used with great success for organizing mixture components into homogenous groups. But the results are limited to normal mixtures. Beyond the clustering application existing research in this area has provided fundamental results regarding the upper bound of the number of modes, but they too are limited to normal mixtures. In this project, we wish to explore the modality of non-normal distributions and their application to real life problems

Regular seminars relevant to the group are held as part of the Statistics seminar series. The seminars cover various aspects across the AI3 initiative and usually span multiple groups. You can find more information on the Statistics seminar series page, where you can also subscribe to the seminar series calendar.