Stochastic modelling of spatiotemporal nonlinear diffusion processes with multifractal characteristics. This research is relevant to solute transport and plume evolution in heterogeneous media. Detailed modelling of these processes is computer-intensive, while the diffusion models of this project offer a more economical alternative. Our study will also benefit the research on the salinity problem. Excessive demand for irrigation water to support agricultural production has stretched freshwater a ....Stochastic modelling of spatiotemporal nonlinear diffusion processes with multifractal characteristics. This research is relevant to solute transport and plume evolution in heterogeneous media. Detailed modelling of these processes is computer-intensive, while the diffusion models of this project offer a more economical alternative. Our study will also benefit the research on the salinity problem. Excessive demand for irrigation water to support agricultural production has stretched freshwater aquifers beyond their long-term yield. Large areas of land have been lost to saltwater intrusion. This proposal will provide suitable tools to predict the level and movement of saltwater in the aquifers. Application to the development of management strategies would bring direct benefit to coastal areas where salinity is a sustainability issue.Read moreRead less
The improvement of climate change investigations by developing and applying innovative evolutionary subset time series modelling using semi-parametric sparse-patterned approaches. With an estimated US$6.98 trillion loss indicated in the Stern review, severe climate change will make world climate conditions harsher and more likely include large natural climate disasters. The health of the Australian economy is critically dependent on decisions of environmental managers. However, most problems of ....The improvement of climate change investigations by developing and applying innovative evolutionary subset time series modelling using semi-parametric sparse-patterned approaches. With an estimated US$6.98 trillion loss indicated in the Stern review, severe climate change will make world climate conditions harsher and more likely include large natural climate disasters. The health of the Australian economy is critically dependent on decisions of environmental managers. However, most problems of complexity arising in climate change involve issues on which we do not possess a deep understanding. This project draws upon a set of inter-disciplinary concepts and models centred in neural networks that enable us to advance our understanding of complexity, leading to superior quantitative tools and models to allow for improved environmental decision-making.
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Improved Monte Carlo Methods for Estimation, Optimisation and Counting. The project will benefit the Australian society by building the theoretical and methodological foundations for the next generation of Monte Carlo techniques. The advancement of the knowledge in this area will provide important tools for solving complex estimation, optimisation and counting problems in engineering, statistics, computer science, mathematics and the physical and life sciences. As a result it will generate a com ....Improved Monte Carlo Methods for Estimation, Optimisation and Counting. The project will benefit the Australian society by building the theoretical and methodological foundations for the next generation of Monte Carlo techniques. The advancement of the knowledge in this area will provide important tools for solving complex estimation, optimisation and counting problems in engineering, statistics, computer science, mathematics and the physical and life sciences. As a result it will generate a competitive advantage for various sections of the Australian industry, including telecommunications, biotechnology and finance. The project will enable Australian researchers to continue to work at the forefront of this fast moving and exciting area of international research.Read moreRead less
A multi-scale approach for modelling coupled transport in heterogeneous and anisotropic porous media. Mathematical Sciences foster interdisciplinary collaboration and underpin fundamental understanding of significant national/international research priorities in science and technology. This world-class team will advance knowledge in modelling complex systems ensuring the competitiveness of Australian research in this important field. A key outcome is a multi-scale computational strategy that can ....A multi-scale approach for modelling coupled transport in heterogeneous and anisotropic porous media. Mathematical Sciences foster interdisciplinary collaboration and underpin fundamental understanding of significant national/international research priorities in science and technology. This world-class team will advance knowledge in modelling complex systems ensuring the competitiveness of Australian research in this important field. A key outcome is a multi-scale computational strategy that can be used by engineers in Australia and France to simulate transport phenomena in porous media, which have significant environmental impact. The research will lead to publications in scientific journals and communications at national/international conferences. Research training of postdocs and PhD students is another excellent outcome of the project.Read moreRead less
Rare Event Simulation with Heavy Tails. The project provides a rigorous way to enhance our understanding of the mechanisms that bring about catastrophic rare events such as urban flooding, electricity shortages and financial bankrupcy. Australia is at the forefront of exciting recent developments in rare event simulation. The advancement of the knowledge in this area will generate a competitive advantage for various sections of the Australian industry, including the areas of industrial reliabili ....Rare Event Simulation with Heavy Tails. The project provides a rigorous way to enhance our understanding of the mechanisms that bring about catastrophic rare events such as urban flooding, electricity shortages and financial bankrupcy. Australia is at the forefront of exciting recent developments in rare event simulation. The advancement of the knowledge in this area will generate a competitive advantage for various sections of the Australian industry, including the areas of industrial reliability, finance and insurance, were accurate simulation techniques are becoming increasingly important.Read moreRead less
Statistical estimation and approximation of anomalous diffusion. This project investigates diffusion processes with long memory, heavy-tailed distributions and higher-order information. Each of these characteristics has been a subject of extensive current research. These processes arise in important applications with significant social/economic benefits such as heat conduction and fluid flow in porous media, propagation of seismic waves, transport of drug molecules in living tissues. Built on ou ....Statistical estimation and approximation of anomalous diffusion. This project investigates diffusion processes with long memory, heavy-tailed distributions and higher-order information. Each of these characteristics has been a subject of extensive current research. These processes arise in important applications with significant social/economic benefits such as heat conduction and fluid flow in porous media, propagation of seismic waves, transport of drug molecules in living tissues. Built on our recent fundamental developments of fractional generalised random fields and fractional diffusion equations, this project tackles the key problems of statistical estimation, approximation and prediction of diffusion processes with all the above characteristics in a unified framework not provided by other approaches.Read moreRead less
Bayesian Statistical Inference for Implicitly defined Probability Models. Bayesian statistics has recently been used to provide solutions for a large number of hitherto intractable problems in science and technology. The success of Bayesian statistics has mainly been due to the application of so-called Markov chain Monte Carlo computational techniques. We aim to improve these algorithms, by providing fast, simple and efficient computational implementations. We will use the results to give ins ....Bayesian Statistical Inference for Implicitly defined Probability Models. Bayesian statistics has recently been used to provide solutions for a large number of hitherto intractable problems in science and technology. The success of Bayesian statistics has mainly been due to the application of so-called Markov chain Monte Carlo computational techniques. We aim to improve these algorithms, by providing fast, simple and efficient computational implementations. We will use the results to give insight by carefully quantifying and modelling uncertainty for such topics as the transmission rate of infectious diseases, the spatial distribution of plant and animal species, investigating biological theory for the genome of a virus, and changes in human fertility.Read moreRead less
The prediction of sleep/wake behaviour based on physiological and social factors. The prevalence of shiftwork has increased in Australia over the last few decades. Shiftworkers obtain less sleep, have greater difficulty maintaining good relationships, have poorer health, and are more likely to be injured at work than others. Using the largest dataset of its kind, we will substantially contribute to understanding the relationships between work hours, sleep, performance and safety. Ultimately, the ....The prediction of sleep/wake behaviour based on physiological and social factors. The prevalence of shiftwork has increased in Australia over the last few decades. Shiftworkers obtain less sleep, have greater difficulty maintaining good relationships, have poorer health, and are more likely to be injured at work than others. Using the largest dataset of its kind, we will substantially contribute to understanding the relationships between work hours, sleep, performance and safety. Ultimately, the project will answer a question critical to workplace safety - how much time off between shifts is needed to be alert and safe at work? The project will also produce tools to help industry design fatigue-friendly rosters, improving the safety, productivity and general well-being of shiftworkers in Australia and overseas.Read moreRead less
New approaches to the statistical modelling of financial risk: combining structural information with flexible, computationally-intensive non-parametric methods. The aims of this project are to provide a range of novel, rigorous, flexible, statistical methods to assess portfolio risk, with due attention to behaviour of its constituent components; to obtain greater understanding of the complexities of risk; and to give students research training in the nexus of statistics and finance. The anticip ....New approaches to the statistical modelling of financial risk: combining structural information with flexible, computationally-intensive non-parametric methods. The aims of this project are to provide a range of novel, rigorous, flexible, statistical methods to assess portfolio risk, with due attention to behaviour of its constituent components; to obtain greater understanding of the complexities of risk; and to give students research training in the nexus of statistics and finance. The anticipated outcomes of this project will be detailed knowledge of extremal behaviour in portfolios, improved methods for calibrating risk, advances in non-parametric methods in finance, a prototype practitioner toolkit for assessing risk, and high-calibre graduates to contribute to Australia's research capacity.Read moreRead less
Cross-Entropy Methods in Complex Biological Systems. The Cross-Entropy method provides a powerful new way to find superior solutions to complicated optimisation problems in biology, ranging from better design and implementation of medical treatments to an increased understanding of complex ecosystems.