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
Investment Approaches and Applications in Financial Markets: Evolutionary Kernel Based Subset Time-Series Using Semi-Parametric Approaches. The project will develop new investment assessments based on subset time-series modeling. Innovative evolutionary kernel smoothing algorithms using semi-parametric approaches will be introduced. The project will make three important applications of this modeling in financial markets: a) benchmarking and evaluation of inflation-indexed bonds; b) evaluation of ....Investment Approaches and Applications in Financial Markets: Evolutionary Kernel Based Subset Time-Series Using Semi-Parametric Approaches. The project will develop new investment assessments based on subset time-series modeling. Innovative evolutionary kernel smoothing algorithms using semi-parametric approaches will be introduced. The project will make three important applications of this modeling in financial markets: a) benchmarking and evaluation of inflation-indexed bonds; b) evaluation of the performance of global diversified investment funds; and c) prediction to provide early warning of the emergence of destabilising deflation or inflation. These three applications will lead to improved risk management practices and investment performance. Recursive algorithms will provide new statistical methods to study investment asset price movements and market volatility.
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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
Efficient Estimation of Statistical Models with Many Parameters. Statistical models are used extensively in business, engineering and the sciences to describe the behavior of systems subject to uncertainty. There are often many unknowns in such models and relatively little data to estimate them. The object of the research is to develop methods that make these statistical models practical to use. The research team will apply the methodology to solve problems in economics, finance, marketing and t ....Efficient Estimation of Statistical Models with Many Parameters. Statistical models are used extensively in business, engineering and the sciences to describe the behavior of systems subject to uncertainty. There are often many unknowns in such models and relatively little data to estimate them. The object of the research is to develop methods that make these statistical models practical to use. The research team will apply the methodology to solve problems in economics, finance, marketing and the analysis of gene expression data. The project will also train doctoral and postdoctoral students and enhance Australia's reputation for research excellence in the Statistical and Mathematical Sciences. 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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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
Saddlepoint approximation, likelihood analysis and ancestral graphs for strong and weak natural selection, genetic drift and population subdivision. Building new research strength in theoretical population genetics and related statistical techniques will enhance Australia's capability in harnessing the power of post-genomic information. Sophisticated statistical techniques that make smart use of genetic data are being developed in this project. The extent to which natural selection and migrati ....Saddlepoint approximation, likelihood analysis and ancestral graphs for strong and weak natural selection, genetic drift and population subdivision. Building new research strength in theoretical population genetics and related statistical techniques will enhance Australia's capability in harnessing the power of post-genomic information. Sophisticated statistical techniques that make smart use of genetic data are being developed in this project. The extent to which natural selection and migration affect current genetic polymorphism on a population level can be quantified using these new methods. New modeling provides a rigorous foundation with which to construct inference techniques currently beyond computational approaches to the data. Assessing selective effects on genetic mutations associated with human disease will be a consequence of this new statistical methodology.Read moreRead less
Investment approaches and opportunities in renewable energy and financial resource markets, using semi-parametric approaches to evolutionary subset time-series lattice-ladder modelling. The project findings will help Australian exporters and importers understand and manage energy and resource price risks more effectively. The investment community will benefit through selecting optimal asset allocations and enhancing value to investors. It will also benefit many other agencies, particularly in th ....Investment approaches and opportunities in renewable energy and financial resource markets, using semi-parametric approaches to evolutionary subset time-series lattice-ladder modelling. The project findings will help Australian exporters and importers understand and manage energy and resource price risks more effectively. The investment community will benefit through selecting optimal asset allocations and enhancing value to investors. It will also benefit many other agencies, particularly in the service industries. It is not well recognised that in developed countries, including Australia, the financial service and related sectors account for more than 60 percent of economic activity and employment, so it is critical that more sophisticated statistical methods be established, and practical applications conducted, in order to advance the understanding of complexity management in the financial service and related sectors.Read moreRead less
NONPARAMETRIC STATISTICS. Nonparametric statistical methods are techniques that implicitly choose statistical models from exceptionally large and highly adaptive classes. The project aims to develop innovative and practicable nonparametric methods in four areas: Statistical Smoothing, Data Mining, Mixture Methods and Robust Inference. The significance of the work lies in its novelty, the breadth of its practical motivation, and its position at the leading edge of contemporary work in statisti ....NONPARAMETRIC STATISTICS. Nonparametric statistical methods are techniques that implicitly choose statistical models from exceptionally large and highly adaptive classes. The project aims to develop innovative and practicable nonparametric methods in four areas: Statistical Smoothing, Data Mining, Mixture Methods and Robust Inference. The significance of the work lies in its novelty, the breadth of its practical motivation, and its position at the leading edge of contemporary work in statistics. Expected outcomes include new technologies for data analysis.Read moreRead less
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