New and computationally feasible methods of constructing efficient and exact confidence limits from count data. Biological and health science data is commonly in the form of counts. The statistical analysis of such data should be (a) efficient i.e. it should not, in effect, throw away valuable data, (b) exact i.e. it should have precisely known statistical properties and (c) computationally feasible. Kabaila and Lloyd (1997-2001) have proposed and analysed a radically new method of confidence li ....New and computationally feasible methods of constructing efficient and exact confidence limits from count data. Biological and health science data is commonly in the form of counts. The statistical analysis of such data should be (a) efficient i.e. it should not, in effect, throw away valuable data, (b) exact i.e. it should have precisely known statistical properties and (c) computationally feasible. Kabaila and Lloyd (1997-2001) have proposed and analysed a radically new method of confidence limit construction which, for the first time, possesses all of these requirements. The purpose of the project is to establish further theoretical support for the new method, to develop efficient computational algorithms and to write easy-to-use computer programs for its practical use.Read moreRead less
Theory and Applications of Computer-Intensive Statistical Methods. The availability of powerful computing equipment has had a dramatic impact on statistical methods and thinking. It has motivated development of novel approaches to data analysis, whose conception
and appreciation, even their application, often demand sophisticated and complex theoretical methods. In this context, the project will develop new approaches to solving non-standard statistical problems. These techniques will eithe ....Theory and Applications of Computer-Intensive Statistical Methods. The availability of powerful computing equipment has had a dramatic impact on statistical methods and thinking. It has motivated development of novel approaches to data analysis, whose conception
and appreciation, even their application, often demand sophisticated and complex theoretical methods. In this context, the project will develop new approaches to solving non-standard statistical problems. These techniques will either have direct application to solving practical problems of national or community concern, or provide a better understanding of the nature of such problems.Read moreRead less
Inverse and related problems in statistics. Modern statistical inverse problems arise in fields from astronomy and biology to engineering and finance. Sometimes the problems involve the analysis of small samples of very high dimensional data, and are central to information aquisition in areas such as genomics and signal analysis. All these topics are of significant national importance, and their solution will bring national and community benefits. In addition, the program to which the proposa ....Inverse and related problems in statistics. Modern statistical inverse problems arise in fields from astronomy and biology to engineering and finance. Sometimes the problems involve the analysis of small samples of very high dimensional data, and are central to information aquisition in areas such as genomics and signal analysis. All these topics are of significant national importance, and their solution will bring national and community benefits. In addition, the program to which the proposal will lead will be used extensively for research training. In Australia, where the demand for research-trained statisticians greatly exceeds supply, this contribution to the nation and the community will be particularly important. Read moreRead less
New Directions in Bayesian Statistics: formulation, computation and application to exemplar challenges. Bayesian statistics is a fundamental statistical and machine learning approach for density estimation, data analysis and inference. However, there remain open questions regarding the formulation of the model, the likelihood and priors, and efficient computation. This project proposes new approaches that address these issues, and applies them to two exemplar challenges: the impact of climate ch ....New Directions in Bayesian Statistics: formulation, computation and application to exemplar challenges. Bayesian statistics is a fundamental statistical and machine learning approach for density estimation, data analysis and inference. However, there remain open questions regarding the formulation of the model, the likelihood and priors, and efficient computation. This project proposes new approaches that address these issues, and applies them to two exemplar challenges: the impact of climate change on the Great Barrier Reef and better understanding neurological diseases related aging, in particular Parkinson's Disease. Read moreRead less
Theory and application of computer-intensive, nonparametric statistical methods. The availability of increasingly powerful computing equipment continues to have a dramatic impact on statistical methods and thinking. These developments, combined with new technologies for generating data, are driving substantial changes in statistics, ranging from the types of problems being solved to the sorts of methods used to solve them. Both the problems and their solutions are of substantial national and c ....Theory and application of computer-intensive, nonparametric statistical methods. The availability of increasingly powerful computing equipment continues to have a dramatic impact on statistical methods and thinking. These developments, combined with new technologies for generating data, are driving substantial changes in statistics, ranging from the types of problems being solved to the sorts of methods used to solve them. Both the problems and their solutions are of substantial national and community benefit. They will be the subject of high-level research supported by this proposal. Read moreRead less
Nonparametric Statistical Methods -- New Directions, Theory and Applications. The research program will take Australia to the forefront of contemporary work in nonparametric statistics, and assist greatly in the training of a new generation of Australian statistical scientists. It will contribute significantly to restoring the health of this strategically important field, in Australian universities and in the nation more generally. The projects outlined in the proposal address problems arising ....Nonparametric Statistical Methods -- New Directions, Theory and Applications. The research program will take Australia to the forefront of contemporary work in nonparametric statistics, and assist greatly in the training of a new generation of Australian statistical scientists. It will contribute significantly to restoring the health of this strategically important field, in Australian universities and in the nation more generally. The projects outlined in the proposal address problems arising in astronomy, economics, engineering, defence, health and image analysis, but the potential areas of impact are broader even than this. This diversity illustrates the extraordinary potential, and strategic significance, of statistics to Australia. Read moreRead less
Modelling with stochastic differential equations. We will develop methodology for modelling and analysis of phenomena subjected to random and uncertain influences, such as behaviour of investors in the market, evolution of economy, values of stocks and ant colonies. This methodology will enable scientists to achieve more accurate description and analysis of their models and provide better understanding of these phenomena. Creating the tools for understanding such complex systems will have far re ....Modelling with stochastic differential equations. We will develop methodology for modelling and analysis of phenomena subjected to random and uncertain influences, such as behaviour of investors in the market, evolution of economy, values of stocks and ant colonies. This methodology will enable scientists to achieve more accurate description and analysis of their models and provide better understanding of these phenomena. Creating the tools for understanding such complex systems will have far reaching benefits both nationally and internationally and will allow Australia to strengthen its position in international research. The project will also provide for postgraduate training and international scientific exchange.Read moreRead less
Stochastic systems with applications to Biology and Finance. This project is concerned with stochastic systems. These mathematical systems, which are controlled by statistical uncertainty and variability, have profound importance in the fields of biology and finance. They are recognised worldwide as being of primary scientific importance. Important questions to be examined are: 1) Branching processes in DNA Polymerase Chain Reaction, 2) long term stationarity in metastable systems, and 3) Sto ....Stochastic systems with applications to Biology and Finance. This project is concerned with stochastic systems. These mathematical systems, which are controlled by statistical uncertainty and variability, have profound importance in the fields of biology and finance. They are recognised worldwide as being of primary scientific importance. Important questions to be examined are: 1) Branching processes in DNA Polymerase Chain Reaction, 2) long term stationarity in metastable systems, and 3) Stochastic Volatility in Finance. The answers to these questions will underpin the statistical theory for potential breakthroughs in the respective areas. This project will contribute to the theory and applications of Stochastic Processes, as well as modelling in biology and finance.Read moreRead less
Stochastic methods for studying models of infection and abundance. The outcomes of this project will have immense benefit to Australia. They impact upon two areas of national importance, namely ensuring an environmentally sustainable Australia, and safeguarding Australia. In particular, the project will provide models, methodology and optimal strategies for sustainable use of Australia's biodiversity, for protecting Australia from invasive diseases and pests, and for protecting Australia from te ....Stochastic methods for studying models of infection and abundance. The outcomes of this project will have immense benefit to Australia. They impact upon two areas of national importance, namely ensuring an environmentally sustainable Australia, and safeguarding Australia. In particular, the project will provide models, methodology and optimal strategies for sustainable use of Australia's biodiversity, for protecting Australia from invasive diseases and pests, and for protecting Australia from terrorism and crime. Special focus will be given to the control of invasive species, the control of emerging infections, and the optimal allocation of resources. The current risks posed by invasive diseases and pests, and the alarming rate of destruction of biodiversity, warrant urgent funding of this project.Read moreRead less
Random Discrete Structures: Approximations and Applications. The behaviour of many real world systems can be modelled by random discrete structures evolving over time. For example, the sizes of populations of frogs in some close patches of forests can be modelled as interacting random processes. The aim of the project is to investigate large discrete random structures that arise from real world application in areas such as biology, complex networks and insurance. The proposed project is at the i ....Random Discrete Structures: Approximations and Applications. The behaviour of many real world systems can be modelled by random discrete structures evolving over time. For example, the sizes of populations of frogs in some close patches of forests can be modelled as interacting random processes. The aim of the project is to investigate large discrete random structures that arise from real world application in areas such as biology, complex networks and insurance. The proposed project is at the interface of mathematics and 'big data' applications and so the work of the project aims to provide theoretical and heuristic underpinnings useful in the algorithms and techniques of practitioners. Understanding the applications in the project requires new, broadly applicable methods and developing such is a complementary aim.Read moreRead less