Trans-dimensional and Approximate Bayesian Computation. Many applied scientists in Australia, particularly those in the biological, medical and environmental sciences are now interested in incorporating Bayesian statistical methodologies into their research.
The development of more generic and efficient Bayesian statistical methods will not only benefit applied statisticians but also the more occasional users of statistics in other disciplinary areas. The success of this project will enhance Au ....Trans-dimensional and Approximate Bayesian Computation. Many applied scientists in Australia, particularly those in the biological, medical and environmental sciences are now interested in incorporating Bayesian statistical methodologies into their research.
The development of more generic and efficient Bayesian statistical methods will not only benefit applied statisticians but also the more occasional users of statistics in other disciplinary areas. The success of this project will enhance Australia's reputation as a strong contributor to the development of Bayesian methodologies. Two PhD students will also be provided training in computational Bayesian statistics.Read moreRead less
Finite Markov chains in statistical mechanics and combinatorics. Finite Markov chains can be viewed as random walks in a finite set. In applications, this set often consists of certain combinatorial objects whose typical properties are to be understood. If the set is large, obtaining exact solutions to such problems is generally infeasible. Markov chains can provide a highly efficient method to generate randomised approximations in such cases, but only if they equilibrate at a rate that grows sl ....Finite Markov chains in statistical mechanics and combinatorics. Finite Markov chains can be viewed as random walks in a finite set. In applications, this set often consists of certain combinatorial objects whose typical properties are to be understood. If the set is large, obtaining exact solutions to such problems is generally infeasible. Markov chains can provide a highly efficient method to generate randomised approximations in such cases, but only if they equilibrate at a rate that grows slowly with the size of the set of objects under study. The project will study several classes of Markov chains that have been developed to study a number of notoriously difficult problems in statistical mechanics and combinatorics, and determine under what conditions they provide efficient approximation schemes.Read moreRead less
Phase transitions in stochastic systems. This project aims to understand models of physical and biological phenomena in the presence of uncertainty/randomness. Such models often exhibit phase transitions if a variable defining the model is modified. For example, a population explosion can occur if the average number of offspring per individual is larger than one, while macroscopic defects can occur in a material if the density of microscopic defects is larger than some threshold. This research c ....Phase transitions in stochastic systems. This project aims to understand models of physical and biological phenomena in the presence of uncertainty/randomness. Such models often exhibit phase transitions if a variable defining the model is modified. For example, a population explosion can occur if the average number of offspring per individual is larger than one, while macroscopic defects can occur in a material if the density of microscopic defects is larger than some threshold. This research could lead to strategies for directing physical and biological systems towards preferred states or phases, and better prediction of adverse events such as fracturing of Antarctic sea ice.Read moreRead less
ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights. In today's world, massive amounts of data in a variety of forms are collected daily from a multitude of sources. Many of the resulting data sets have the potential to make vital contributions to society, business and government, as well as impact on international developments, but are so large or complex that they are difficult to process and analyse using traditional tools. The aim of this ....ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights. In today's world, massive amounts of data in a variety of forms are collected daily from a multitude of sources. Many of the resulting data sets have the potential to make vital contributions to society, business and government, as well as impact on international developments, but are so large or complex that they are difficult to process and analyse using traditional tools. The aim of this Centre is to create innovative mathematical and statistical models that can uncover the knowledge concealed within the size and complexity of these big data sets, with a focus on using the models to deliver insight into problems vital to the Centre's Collaborative Domains: Healthy People, Sustainable Environments and Prosperous Societies.Read moreRead less
Bayesian statistical models for understanding outcomes and improving decision-making for women screened for breast cancer. This project has two key benefits: (i) the development of frontier statistical methods for spatio-temporal analysis and data synthesis, which are imperative in a wide range of disciplines; and (ii) the application of these methods for improved understanding of breast cancer outcomes for women screened in Queensland. The project results will lead to direct health and financi ....Bayesian statistical models for understanding outcomes and improving decision-making for women screened for breast cancer. This project has two key benefits: (i) the development of frontier statistical methods for spatio-temporal analysis and data synthesis, which are imperative in a wide range of disciplines; and (ii) the application of these methods for improved understanding of breast cancer outcomes for women screened in Queensland. The project results will lead to direct health and financial benefits through targeted policies for increasing screening uptake and reducing cancer morbidity and mortality and therefore health spending in this area. Importantly, the project represents an excellent training opportunity to develop a PhD candidate into an experienced interdisciplinary researcher.Read moreRead less
Queueing systems and their application to telecommunication systems and dams. The aim of this project is to investigate the behaviour of large queueing systems under critical load conditions and solve problems related to large telecommunication systems, information technologies and dams. The project will have significant economic and social benefits. It will lead to the solution of high priority problems of optimal control of water resources, as well as problems in design technology of high spee ....Queueing systems and their application to telecommunication systems and dams. The aim of this project is to investigate the behaviour of large queueing systems under critical load conditions and solve problems related to large telecommunication systems, information technologies and dams. The project will have significant economic and social benefits. It will lead to the solution of high priority problems of optimal control of water resources, as well as problems in design technology of high speed telecommunication networks. It will suggest new more profitable approaches to known problems such as effective bandwidth problem, analysis and design of computer networks, optimal control of dams, and anticipate not ordinary results and solutions. It will contribute to the mathematical culture in Australia and worldwide. Read moreRead less
Graph isomorphism and quantisation of longest cycles by means of determinants and spectra. A characterisation of the difficulty of the Hamiltonian cycle problem and the graphs isomorphism problem will be a significant conceptual advancement with repercussions in a number of fields including combinatorial optimisation and theoretical computer science, in particular, the Google PageRank. Applications of tensor networks technique will lead to a design of a quantum computer that enumerates all Hamil ....Graph isomorphism and quantisation of longest cycles by means of determinants and spectra. A characterisation of the difficulty of the Hamiltonian cycle problem and the graphs isomorphism problem will be a significant conceptual advancement with repercussions in a number of fields including combinatorial optimisation and theoretical computer science, in particular, the Google PageRank. Applications of tensor networks technique will lead to a design of a quantum computer that enumerates all Hamiltonian cycles in a graph. Analysis of the determinant objective function in terms of the eigenvalues may lead to new spectral properties of stochastic matrices. Algorithmic advances exploiting such a characterisation will significantly contribute to existing technologies for solving problems in a wide range of applications.Read moreRead less
New Approaches to Modelling and Analysing Long-Memory Random Processes. The project aims to develop new approaches using infinite-dimensional Markov processes to solving important long-standing problems from the theory of long memory random processes and their applications. It aims to: construct a class of new representations of random processes; derive inequalities for the key numerical characteristics; and, devise and investigate numerical methods for computing the characteristics and for perf ....New Approaches to Modelling and Analysing Long-Memory Random Processes. The project aims to develop new approaches using infinite-dimensional Markov processes to solving important long-standing problems from the theory of long memory random processes and their applications. It aims to: construct a class of new representations of random processes; derive inequalities for the key numerical characteristics; and, devise and investigate numerical methods for computing the characteristics and for performing statistical inference on the long memory models. The accuracy of numerical approximations will be analysed using simulations on supercomputers. Expected outcomes include models and results of practical importance with applications such as intrusion detection problems, cell motility for biological data and telecommunication.Read moreRead less
Efficient Design for Generalized Linear Models. In industrial, commercial and social research, we collect data in order to predict the outcome of a process based on the inputs to that process. We want to maximize the information that is gained from the data. Good planning is crucially important to achieve this. This project will determine how best to select the inputs to the process for many situations that occur in research. A computer package to answer these questions will be written. The nati ....Efficient Design for Generalized Linear Models. In industrial, commercial and social research, we collect data in order to predict the outcome of a process based on the inputs to that process. We want to maximize the information that is gained from the data. Good planning is crucially important to achieve this. This project will determine how best to select the inputs to the process for many situations that occur in research. A computer package to answer these questions will be written. The nation will benefit from a fundamental increase in efficiency of research and, therefore, in efficient use of research dollars.Read moreRead less
Complex data, model selection and bootstrap inference. The project will provide new statistical methods and associated software for the analysis and modelling of complex data, as well as quality research training. This project will benefit researchers in statistics and users of statistics who encounter the complex data considered in this project and who need to model and make inferences from these data. Since these kinds of data arise in many areas (such as medicine, genetics, chemistry etc), ....Complex data, model selection and bootstrap inference. The project will provide new statistical methods and associated software for the analysis and modelling of complex data, as well as quality research training. This project will benefit researchers in statistics and users of statistics who encounter the complex data considered in this project and who need to model and make inferences from these data. Since these kinds of data arise in many areas (such as medicine, genetics, chemistry etc), Australia and Australian industry will ultimately benefit from the proposed research. The strengthening of international link and the training of highly trained research scientists in an area of national importance will also benefit Australia.Read moreRead less