Bayesian Inference for Multivariate Hierarchical Regression Models. This project will develop Bayesian methodology for analysing multivariate regression models. The distribution of each measurement can be discrete or continuous, with the dependence between measurements obtained through the correlation matrix of a Gaussian copula. Model parsimony is obtained by identifying zero elements in the correlation matrix or its inverse and by variable selection on the regression parameters. The results wi ....Bayesian Inference for Multivariate Hierarchical Regression Models. This project will develop Bayesian methodology for analysing multivariate regression models. The distribution of each measurement can be discrete or continuous, with the dependence between measurements obtained through the correlation matrix of a Gaussian copula. Model parsimony is obtained by identifying zero elements in the correlation matrix or its inverse and by variable selection on the regression parameters. The results will be applied to solve problems in finance, health management and marketing. In all these fields multiple observations are often taken per individual or time period and the models need to incorporate measures of dependence and uncertainty.Read moreRead less
Asynchronous Continuous Time Conditioning. Methodology for reasoning about Asynchronous Temporal Conditional Events (ATCE) obtains, complete with logical calculus for causal relations, reasoning about continuous time belief change, and markov chain algorithms calculating joint distributions of ATCE's.
Current techniques, including bayesian nets, are oblivious to temporal aspects; within our model they can be enhanced to recognize dynamic time changes. Ours is the first such unified model and ....Asynchronous Continuous Time Conditioning. Methodology for reasoning about Asynchronous Temporal Conditional Events (ATCE) obtains, complete with logical calculus for causal relations, reasoning about continuous time belief change, and markov chain algorithms calculating joint distributions of ATCE's.
Current techniques, including bayesian nets, are oblivious to temporal aspects; within our model they can be enhanced to recognize dynamic time changes. Ours is the first such unified model and first to link conditional objects with continuous time constraints.
Need for structures we propose arises in diagnostic reasoning, bayesian learning, temporal databases, and time-dependent data mining. Several commercial products (like Microsoft Office Assistant)could apply them forthwith.Read moreRead less
Market Model of Implied Volatility. The outcomes of the project will constitute a new methodology with a wide range of tools to handle the market uncertainties with practical applications in the finance industry. Consequently, the benefits of this project to the nation include enhancing its scientific standing in the international community, the training of Australian researchers in forefront methods of modelling of complex stochastic systems and the benefits resulting from its commercially rele ....Market Model of Implied Volatility. The outcomes of the project will constitute a new methodology with a wide range of tools to handle the market uncertainties with practical applications in the finance industry. Consequently, the benefits of this project to the nation include enhancing its scientific standing in the international community, the training of Australian researchers in forefront methods of modelling of complex stochastic systems and the benefits resulting from its commercially relevant elements. Read moreRead less
Joint System Identification for Point Processes and Time-series. In various application areas such as neurophysiology, earthquake modeling, price spikes in electricity markets, the data of interest are point processes (aka sequences of events) or combinations of point processes and analog signals. To understand the underlying subject of interest we need to be able to extract the maximum information from these observation sequences. The current tools for doing this are very limited. This resear ....Joint System Identification for Point Processes and Time-series. In various application areas such as neurophysiology, earthquake modeling, price spikes in electricity markets, the data of interest are point processes (aka sequences of events) or combinations of point processes and analog signals. To understand the underlying subject of interest we need to be able to extract the maximum information from these observation sequences. The current tools for doing this are very limited. This research program will develop the complex signal processing and system methodology needed to create a suitable tool set.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
Boundary Crossing Analysis for Random Processes with Applications to Risk Management. Effective management of environmental, financial and superannuation investment risks is vitally important for Australia. Results of the project will add to the theoretical foundations of risk management and provide new computational tools for specialists working in the areas of financial engineering, insurance, superannuation funds. These tools will assist in improving risk profile evaluation and developing new ....Boundary Crossing Analysis for Random Processes with Applications to Risk Management. Effective management of environmental, financial and superannuation investment risks is vitally important for Australia. Results of the project will add to the theoretical foundations of risk management and provide new computational tools for specialists working in the areas of financial engineering, insurance, superannuation funds. These tools will assist in improving risk profile evaluation and developing new statistical control charts for security monitoring of epidemics, networks intrusions and other potentially dangerous changes. The research will also give Australia a competitive advantage in the area of education related to stochastic processes, mathematical finance, control theory and their applications.Read moreRead less
Large Time Behavior of Solutions to Stochastic Partial Differential Equations. We will study equilibria of complex systems described by stochastic partial differential equations. The rates of convergence to equilibrium will be obtained for the equations driven by Gaussian and general Levy noises under physically relevant assumptions. The benefits of this project to the nation include enhancing its scientific standing in the international community, the training of Australian researchers in foref ....Large Time Behavior of Solutions to Stochastic Partial Differential Equations. We will study equilibria of complex systems described by stochastic partial differential equations. The rates of convergence to equilibrium will be obtained for the equations driven by Gaussian and general Levy noises under physically relevant assumptions. The benefits of this project to the nation include enhancing its scientific standing in the international community, the training of Australian researchers in forefront methods of mathematical analysis of complex systems and development of close ties with the world leaders in this area of research. The project will advance our understanding of complex systems arising in Phyiscs, Engineering, Social and Life Sciences, hence fits into the Priority Goal: Breakthrough Science. Read moreRead less
Fair pricing of superannuation guaranteed benefits with downturn risk. Australians have more than $2.7 trillion in superannuation assets, meaning that Australia is the fourth largest holder of pension fund assets worldwide. Hence the impact of market fluctuations on financial well-being of retirees can be detrimental, especially during market downturns associated with economic crises. The finance industry addresses this issue by complementing variable annuities with riders designed to protect th ....Fair pricing of superannuation guaranteed benefits with downturn risk. Australians have more than $2.7 trillion in superannuation assets, meaning that Australia is the fourth largest holder of pension fund assets worldwide. Hence the impact of market fluctuations on financial well-being of retirees can be detrimental, especially during market downturns associated with economic crises. The finance industry addresses this issue by complementing variable annuities with riders designed to protect the income stream of retirees. This project aims to develop a novel approach to fair pricing and optimal withdrawals and surrender policies for superannuation guaranteed benefit products through a comprehensive analysis of complex optimisation problems in stochastic models of financial markets with downturn risk.Read moreRead less
Modelling and estimation techniques for the transmission and control of Tuberculosis with new and existing vaccines. Most Tuberculosis in Australia is seen in foreign-born people. Australia has an important role in providing leadership in the Asia-Pacific region in Tuberculosis control, which will have flow-on benefits to TB control in this country. Using mathematical models, this project will assess the use of vaccines for Tuberculosis in the developing world. Rising levels of extremely drug r ....Modelling and estimation techniques for the transmission and control of Tuberculosis with new and existing vaccines. Most Tuberculosis in Australia is seen in foreign-born people. Australia has an important role in providing leadership in the Asia-Pacific region in Tuberculosis control, which will have flow-on benefits to TB control in this country. Using mathematical models, this project will assess the use of vaccines for Tuberculosis in the developing world. Rising levels of extremely drug resistant infections make this a timely and important study with significant policy implications, both externally and in the Australian context. Read moreRead less
Statistical Methods for Flow Cytometric Data. The project will aid users of flow cytometry throughout Australia. It will help foster collaborations between the biological and mathematical scientists. Biological research is an important part of Australia's future and is becoming very quantitative. During the course of the project, two PhD students will be provided strong training in Statistics geared towards biological applications. The project is aligned with the 8th Human Leucocyte Differentiat ....Statistical Methods for Flow Cytometric Data. The project will aid users of flow cytometry throughout Australia. It will help foster collaborations between the biological and mathematical scientists. Biological research is an important part of Australia's future and is becoming very quantitative. During the course of the project, two PhD students will be provided strong training in Statistics geared towards biological applications. The project is aligned with the 8th Human Leucocyte Differentiation Antigen workshop to culminate in Adelaide in December 2004 and will aid the fight against blood cell cancers. The project will also aid research on plankton with potential commercial benefits for Australia's marine scallop industry.
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