Statistics is an essential part of science, providing the mathematical languageand techniques necessary for understanding and dealing with chance and uncertainty in nature. Statistics involves the design, collection, analysis and interpretation of numerical data, with the aim of extracting patterns and other useful information. Examples include the analysis of DNA and protein sequences, the construction of evolutionary trees from genetic data, the improvement of medical treatments via experimental designs, and the assessment of drought conditions through meteorological data. A main feature of statistics is the development and use of statistical and probabilistic models for random phenomena, which can be analysed and used to make principled predictions and decisions. Examples of such models can be found in biology (genetics, population modelling), finance (stock market fluctuations, insurance claims), physics (quantum mechanics/computing), medicine (epidemiology, spread of HIV/AIDS), telecommunications (internet traffic, mobile phone calls), and reliability (safety of oil rigs, aircraft failure), to name but a few.

The Probability and Statistics Group is recognised internationally for its active and dynamic research programs across a number of areas of statistics and has research strengths in several areas including bioinformatics, biostatistics, computational statistics, discriminant and cluster analyses, experimental design, image analysis, machine learning, mixture modelling, Monte Carlo simulation, multivariate analysis, and applied probability and stochastic processes. The Group has established ongoing collaborations with other disciplines, particularly in the biological and medical sciences, bioinformatics, engineering and information technology, as well as with industry and government bodies.    
 

Available Projects

Suitable for:  Third year and honours-level students in statistics, mathematics and/or computer science.  Familiarity with R or Matlab is highly desirable.

Project:  A novel application of generalised linear models is in the power rankings...

Ms Janet Seddon

Traditional models of player valuation in Rugby League use summary statistics to estimate the value of a player.  Some examples include: minutes played, tackles made, tackles missed, hit ups made, metres gained, tries scored, try assists, errors, penalties conceded and kick effectiveness....

Dr Michael Forbes

 

 

The Centre for Applications in Natural Resource Mathematics (CARM) is a School Centre in the School of Mathematics and Physics at The University of Queensland. The Centre is co-funded by...

Professor Jerzy Filar
As our world is becoming more and more complex, Statistics remains the most principled way to make some sense of all this randomness. A quote by Hal Varian, Chief economist at Google, conveys a lot about the current relevance of statistics:
 
“I keep saying...
Professor Dirk Kroese
Many real-world quantitative problems are solved nowadays through Monte Carlo methods: that is, through random experiments on a computer....
Professor Dirk Kroese

Count data often exhibit deviations from a nominal Poisson distribution. This project will look at ways to handle such deviations, both parametrically and non-parametrically.

Dr Alan Huang

Why are seven shuffles enough to randomise a deck of cards (Bayer & Diaconis, 1992)? Can we extend this result to other types of shuffles? What other random processes can we...

Dr Alan Huang

In 2007, B. Bollobas, S. Janson, and O. Riordan published an important paper titled ``The Phase Transition in Inhomogeneous Random Graphs,'' which gives properties of a very...

Dr Thomas Taimre

Random networks are often modelled without reference the particular space which they inhabit.  There is some work in this area (for example Penrose’s Random Geometric...

Dr Thomas Taimre

In many social networks, selection of friends on the basis of social status is very common. Similarly, websites may link to more popular websites in the hope of gaining more traffic. Simple models of these phenomena, where the benefits of connection vary according to some metric (for example...

Dr Thomas Taimre

Many networks from crystalline lattices to social networks display so-called self-organizing phenomena. This essentially means that global order or chaos can emerge from simple local rules.  Particular interest has been paid to these phenomena in light of residential segregation in the US...

Dr Thomas Taimre

The properties of complex networks are difficult to study without the aid of simulation, and so efficient and reliable simulation techniques for random networks are of great interest.  Two such methods are degree distributions and graph motifs.

In this project, you will investigate...

Dr Thomas Taimre

Stochastic game theory is the study of strategic interactions between actors in an environment where their payoffs are affected by the actions of all players in the past.

In this project, you will investigate in simulation simple models for stochastic network games, where the environment...

Dr Thomas Taimre

Social, economic, and infrastructure networks are crucially important to today's increasingly connected world.  In this project you will investigate how to estimate models of dynamic networks and conduct inference for these...

Dr Thomas Taimre

The Poisson lily-pond model is a spatial germ--grain process, whose ``germs'' are points of a Poisson process with ``grains'' growing at uniform rate from these germs, stopping when their boundaries touch.  While some results regarding the size of the largest connected...

Dr Thomas Taimre

A diffusion process on a Riemannian manifold has infinitesimal generator which is fundamentally related to the Laplace--Beltrami operator on that manifold.  For a...

Dr Thomas Taimre

The excess-phase model for interferometric signals is a simple model which well captures much of the complex behaviour observed in laser interferometers. ...

Dr Thomas Taimre

Mixture models are a powerful tool for many statistical applications, including density estimation from data.  
This project focuses on using mixture models in sequential or on-line importance sampling.  A specific application of interest is to the estimation of rare events,...

Dr Thomas Taimre

Stochastic differential equations driven by Brownian motion or L\'evy processes are well established as models for many real-world phenomena.  Just as there are efficient...

Dr Thomas Taimre

Random sums of random variables arise in many contexts of applied probability such as the probability of buffer overflow in queues, or when considering the probability of ruin for risk models.  When such quantities of interest cannot be evaluated precisely, there are many well established...

Dr Thomas Taimre

Generalized linear models have quickly become indispensable tools for the...

Dr Alan Huang

Generalized linear models have become indispensible tools for the analysis of biomedical, agricultural and engineering data. Recently, there has been some exciting work on novel extensions of generalized linear models that relax...

Professor Joseph Grotowski

Finite mixture distributions have become increasingly popular in the modelling and analysis of data due to their flexibility. This use of finite mixture distributions to model heterogeneous data has undergone...

Professor Geoff McLachlan

This project is concerned with some of the problems and issues associated with the statistical analysis of microarray gene-expression data. One problem concerns the identification of genes that are differentially expressed between different classes containing tissue samples taken from subjects...

Professor Geoff McLachlan

Traditional methods of analysing flow cytometry data rely on subjective manual gating. As modern day machines can now provide data on...

Professor Geoff McLachlan

This project is concerned with the clustering of high-dimensional data where the number of variables is much larger than the number of experimental units.  Consideration is to be given to the suitability and  effectiveness of the use of  factor models to enable normal mixture...

Professor Geoff McLachlan

This project deals with analysis of huge volumes of data recorded on-line for urban road traffic networks, namely Melbourne's traffic system.  There are tens of interesting questions that need to be formulated and answered by means of real data analysis.

Dr Yoni Nazarathy

Standard queueing network models such as the celebrated Jackson and BCMP networks exhibit mathematically elegant product form solutions of the stationary distribution. This means that the problem of evaluating the probabilistic behavior of the network at steady state is typically tractable. As...

Dr Yoni Nazarathy

The study of matrix analytic methods in queueing theory is by now a well established research field. The basic idea is to model queueing phenomena by complex large dimensional Markov chains which are well structured and are thus amenable to efficient algorithmic...

Dr Yoni Nazarathy

Queueing networks are stochastic mathematical models that are often used for analyzing service, manufacturing and communication systems. One often attempts to model the situation at hand by means of a...

Dr Yoni Nazarathy

 

Modelling the behavior of correlated electrons in finite systems is at the heart of theoretical chemistry.  Many sophisticated techniques have been...

Dr Seth Olsen

The field of meta-heuristic optimization offers a variety of powerful methods for solving difficult optimization problems, and requires no prior knowledge other than the cost function and any constraints. These methods include simulated annealing, genetic algorithms, estimation of distribution...

Dr Ian Wood

A variety of assessment methods exist to aid in the choice of an optimal statistical model or the set of explanatory variables to be used with it. The ability to measure and store data increases yearly leading to a growing demand for the analysis of high-dimensional data in many fields e.g....

Dr Ian Wood