Stein's method for probability approximation. Data of counts in time, such as incoming calls in telecommunications and the clusters of palindromes in a family of herpes-virus genomes, arise in an extraordinarily diverse range of fields from science to business. These problems can be modelled by sums of random variables taking values 0 and 1 in probability theory, thus permitting approximate calculations which are often good enough in practice. This project will obtain such approximate solutions ....Stein's method for probability approximation. Data of counts in time, such as incoming calls in telecommunications and the clusters of palindromes in a family of herpes-virus genomes, arise in an extraordinarily diverse range of fields from science to business. These problems can be modelled by sums of random variables taking values 0 and 1 in probability theory, thus permitting approximate calculations which are often good enough in practice. This project will obtain such approximate solutions and estimate the errors involved. Applications include analysis of data in insurance, finance, flood prediction in hydrology.Read moreRead less
Centre for Mathematical and Statistical Modelling of Complex Systems. This Centre, formed by a group of high-profile researchers, brings expertise from linked but hitherto disparate areas together. It will place Australia at the forefront of research into complex systems.
The mission of the Centre is to stimulate research in mathematical and statistical modelling of complex systems and to encourage cross-fertilisation of ideas and techniques. The specific objectives are
- to formulate and ana ....Centre for Mathematical and Statistical Modelling of Complex Systems. This Centre, formed by a group of high-profile researchers, brings expertise from linked but hitherto disparate areas together. It will place Australia at the forefront of research into complex systems.
The mission of the Centre is to stimulate research in mathematical and statistical modelling of complex systems and to encourage cross-fertilisation of ideas and techniques. The specific objectives are
- to formulate and analyse mathematical and statistical models for natural and artificial complex systems,
- to use these models to develop an understanding of the behaviour of these systems
- to incorporate this understanding into strategies for management and control.Read moreRead less
Mathematical studies on the statistical properties of complex systems. Introduced in the late `50's to model nuclear spectra, random matrices are now standard in the theory of quantum chaos, mesoscopic phenomena and disordered systems. These are all examples of physical complex systems, characterized by unknown interactions leading to predictable behaviour due to symmetries. Vast mathematical structures result from the symmetries - integrable systems, Painleve equations, Macdonald polynomial the ....Mathematical studies on the statistical properties of complex systems. Introduced in the late `50's to model nuclear spectra, random matrices are now standard in the theory of quantum chaos, mesoscopic phenomena and disordered systems. These are all examples of physical complex systems, characterized by unknown interactions leading to predictable behaviour due to symmetries. Vast mathematical structures result from the symmetries - integrable systems, Painleve equations, Macdonald polynomial theory to name a few. These structures will be further developed, leading to the analytic form of distribution functions quantifying classes of complex systems. Analogous statistical quantification is the essence of recently proposed methods to analyze artificial complex systems such as the stock market.Read moreRead less
Modelling patient flows through hospitals: optimizing effective use of resources. Hospitals are complex, dynamic systems confronted by increased demand in the face of shrinking real capacity. Managing such systems is currently undertaken with sub-optimal analytical support, particularly when demand and capacity are changing and resources must be manipulated to respond to such changes. In this project, the investigators will apply a mathematical modelling approach to the analysis of hospital pati ....Modelling patient flows through hospitals: optimizing effective use of resources. Hospitals are complex, dynamic systems confronted by increased demand in the face of shrinking real capacity. Managing such systems is currently undertaken with sub-optimal analytical support, particularly when demand and capacity are changing and resources must be manipulated to respond to such changes. In this project, the investigators will apply a mathematical modelling approach to the analysis of hospital patient flows. Furthermore, they will employ statistical process control methodologies to the problem of recognising and responding to changes in the flows, so that performance objectives are met. In doing this, they will give health service managers and clinicians a significant advantage in deciding how best to manage a constrained resource to maximize access, throughput and patient outcomes.Read moreRead less
Multifractal models in finance via the crossing tree. High level mathematical modelling is an established part of the modern finance industry, in particular the Black-Scholes option pricing formula is now an indispensable financial tool.
To remain competitive the Australian financial sector needs to keep up with developments in mathematical finance, which is only possible if the Australian academic community remains active in the field.
The work on multifractal modelling proposed here is innov ....Multifractal models in finance via the crossing tree. High level mathematical modelling is an established part of the modern finance industry, in particular the Black-Scholes option pricing formula is now an indispensable financial tool.
To remain competitive the Australian financial sector needs to keep up with developments in mathematical finance, which is only possible if the Australian academic community remains active in the field.
The work on multifractal modelling proposed here is innovative both in its theoretical aspects and its applied methodology, and will ensure that Australian research remains at the cutting edge of this highly competitive and fast moving field.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
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
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
New Stochastic Processes with Applications in Finance. This project investigates the properties and the use of two new families of models with applications in Finance, and beyond. It will contribute to the development of fundamental research in mathematics and its applications. The project will produce more realistic financial models that will benefit researchers in this field. This will in turn have a flow on effect to benefit the wider community. The project will provide for postgraduate train ....New Stochastic Processes with Applications in Finance. This project investigates the properties and the use of two new families of models with applications in Finance, and beyond. It will contribute to the development of fundamental research in mathematics and its applications. The project will produce more realistic financial models that will benefit researchers in this field. This will in turn have a flow on effect to benefit the wider community. The project will provide for postgraduate training and international scientific exchange. Overall, the project will strengthen Australia's standing at the forefront of fundamental and applied research.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