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
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
Bayesian Inference for Flexible Parametric Multivariate Econometric Modelling. The anticipated outcomes include the development of enhanced multivariate econometric models and innovative computationally intensive methods for their estimation. These models are used in numerous and diverse applications which are data-intensive and where more complete models will greatly enhance data-based decision-making. Results include improved information use in the wholesale electricity markets, in financial m ....Bayesian Inference for Flexible Parametric Multivariate Econometric Modelling. The anticipated outcomes include the development of enhanced multivariate econometric models and innovative computationally intensive methods for their estimation. These models are used in numerous and diverse applications which are data-intensive and where more complete models will greatly enhance data-based decision-making. Results include improved information use in the wholesale electricity markets, in financial market investment decision-making and for the assessment of the impact of internet advertising.Read moreRead less
Bayesian estimation of flexible spatial models with applications in medical imaging and econometric modeling. This project aims to develop statistical methodology for estimating flexible highly parameterised Bayesian spatial models. The flexible models examined will include regression, choice and time series models for data that is spatially registered. Spatial smoothing of parameters in the models will involve application of hierarchical spatial prior distributions. The resulting methodology wi ....Bayesian estimation of flexible spatial models with applications in medical imaging and econometric modeling. This project aims to develop statistical methodology for estimating flexible highly parameterised Bayesian spatial models. The flexible models examined will include regression, choice and time series models for data that is spatially registered. Spatial smoothing of parameters in the models will involve application of hierarchical spatial prior distributions. The resulting methodology will be applied to the analysis of medical imaging data and to the estimation of spatial econometric models of residential real estate prices. The expected outcomes include developments in the frontier framework of Bayesian computational estimation methodology, improved methods for medical image processing and estimation of high resolution spatial models of residential real estate prices in Australian metropolitan centres.Read moreRead less
Seasonal adjustment using disaggregated short time span data. Seasonally adjusted economic and social times series are vital information used by governments and businesses in decision making. This project will develop statistical methods to estimate and remove seasonal factors from economic and social time series using finely disaggregated data for a relatively small number of time periods. This will enable better and quicker estimation of seasonal factors when new series are introduced or there ....Seasonal adjustment using disaggregated short time span data. Seasonally adjusted economic and social times series are vital information used by governments and businesses in decision making. This project will develop statistical methods to estimate and remove seasonal factors from economic and social time series using finely disaggregated data for a relatively small number of time periods. This will enable better and quicker estimation of seasonal factors when new series are introduced or there a major changes to existing series, improving the analysis of such series and the decisions based on them.Read moreRead less
Continued Fractions and Torsion on Hyperelliptic Curves. Scientific advance should not blindly add to our knowledge; a true advance brings insights that collapse different issues into one. Understanding more is to need to remember less. For an important class of examples, this project identifies the study of a fundamental invariant of a quadratic number field, its regulator and hence its class number, with maximum torsion on the Jacobian variety of an hyperelliptic curve. The investigator's meth ....Continued Fractions and Torsion on Hyperelliptic Curves. Scientific advance should not blindly add to our knowledge; a true advance brings insights that collapse different issues into one. Understanding more is to need to remember less. For an important class of examples, this project identifies the study of a fundamental invariant of a quadratic number field, its regulator and hence its class number, with maximum torsion on the Jacobian variety of an hyperelliptic curve. The investigator's methods will surprise some longstanding problems into submission and in particular will lead them to reveal full data on torsion on hyperelliptic curves of low genus.
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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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Who acquires infection from whom across international borders? New approaches for control of emerging infections through understanding travel patterns. Mathematical modelling of data on travellers traversing Australia's borders and their contact patterns can be used to understand the pathways by which infectious diseases enter and spread in Australia. Currently available social contact data which informs models are inadequate and outdated. Gathering new data relevant to modern society will help ....Who acquires infection from whom across international borders? New approaches for control of emerging infections through understanding travel patterns. Mathematical modelling of data on travellers traversing Australia's borders and their contact patterns can be used to understand the pathways by which infectious diseases enter and spread in Australia. Currently available social contact data which informs models are inadequate and outdated. Gathering new data relevant to modern society will help control future infectious disease threats to our society. Our aim is to collect detailed, unique data on demography, behavioural and social patterns of travellers and residents, and use this to develop mathematical models to evaluate effective control measures for emerging infections in Australia. This study will make a unique contribution to national disease control policy.Read moreRead less
A formal foundation for security architecture. Security of computer systems is essential for the maintenance of privacy, confidentiality and integrity of personal, commercial and government data, and the trustworthiness of the computational devices that are embedded in critical societal infrastructure. However, current theoretical understanding of secure systems development is poor. The project will develop our understanding of an emerging approach to the design of secure systems and develop ver ....A formal foundation for security architecture. Security of computer systems is essential for the maintenance of privacy, confidentiality and integrity of personal, commercial and government data, and the trustworthiness of the computational devices that are embedded in critical societal infrastructure. However, current theoretical understanding of secure systems development is poor. The project will develop our understanding of an emerging approach to the design of secure systems and develop verification methods that may be applied to guarantee systems security. Its outcomes will contribute to processes for certifying systems at very high levels of security, a requirement in defence and government settings that will become increasingly significant in the commercial sector.Read moreRead less
Mathematics of Elliptic Curve Cryptography. The Australian society and economy requires fast, reliable, and secure digital infrastructure. First-generation security solutions cannot support the efficiency and scalability requirements of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined and analysed. Thus developing a new framework in this area is one of the most important and urgent tasks. Besides, the intended wor ....Mathematics of Elliptic Curve Cryptography. The Australian society and economy requires fast, reliable, and secure digital infrastructure. First-generation security solutions cannot support the efficiency and scalability requirements of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined and analysed. Thus developing a new framework in this area is one of the most important and urgent tasks. Besides, the intended work advances our knowledge of the theory and the quality of our culture. As such, it will promote the Australian science and will also have many practical applications in Computer Security and E-Commerce.Read moreRead less