Regularisation methods of inverse problems: theory and computation. This project aims to investigate regularisation methods for inverse problems which are ill-posed in the sense that their solutions depend discontinuously on the data. When only noisy data is available, regularisation methods define stable approximate solutions by replacing the original inverse problem with a family of well-posed neighbouring problems monitored by a so-called regularisation parameter. The project expects to devel ....Regularisation methods of inverse problems: theory and computation. This project aims to investigate regularisation methods for inverse problems which are ill-posed in the sense that their solutions depend discontinuously on the data. When only noisy data is available, regularisation methods define stable approximate solutions by replacing the original inverse problem with a family of well-posed neighbouring problems monitored by a so-called regularisation parameter. The project expects to develop purely data-driven rules to choose the regularisation parameter and show how they work in theory, and in practice. It will also develop convex framework, acceleration strategies as well as preconditioning and splitting ideas to design efficient regularisation solvers.Read moreRead less
Solving inverse problems with Iterative regularisation and convex penalties. This project aims to develop and investigate new computational procedures for the solution of inverse problems which do not have the usual smoothness properties (or source conditions) required for the traditional regularisation methods. Examples of such inverse problems are very common and include image restoration, photo-acoustic tomography and spectroscopy. It is anticipated that this project will substantially extend ....Solving inverse problems with Iterative regularisation and convex penalties. This project aims to develop and investigate new computational procedures for the solution of inverse problems which do not have the usual smoothness properties (or source conditions) required for the traditional regularisation methods. Examples of such inverse problems are very common and include image restoration, photo-acoustic tomography and spectroscopy. It is anticipated that this project will substantially extend the toolbox of methods for such problems utilising ideas from Banach spaces, convex analysis, parallel computing and optimisation. This project is expected to make a substantial contribution to a better understanding of inverse problems and their solution procedures.Read moreRead less
Theory and applications of three dimensional fractal transformations. The purpose of this project is to develop the theory and algorithms for a new class of continuous mappings between fractals. Outcomes include a better understanding of fractals, substantially better algorithms for fractal compression and many new applications.
Sparse grid approximations and fitting using generalised combination techniques. Sparse grid techniques provide an effective tool to deal with the
computational curse of dimensionality which is a constant challenge in
modelling complex data. The proposed research is aimed at the
development and analysis of algorithms for data fitting with sparse
grids using variants of the combination technique. The outcome of the
research is a theory which will provide insights in the applicability,
limit ....Sparse grid approximations and fitting using generalised combination techniques. Sparse grid techniques provide an effective tool to deal with the
computational curse of dimensionality which is a constant challenge in
modelling complex data. The proposed research is aimed at the
development and analysis of algorithms for data fitting with sparse
grids using variants of the combination technique. The outcome of the
research is a theory which will provide insights in the applicability,
limitations and the convergence properties of the proposed
algorithms. The outcomes will be widely applicable in modelling of
large scale and complex data as is encountered in areas of
bioinformatics, physics and experimental studies of complex systems.
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Non-commutative Fractal Geometry: New Invariants. This project capitilises on Australian strengths in mathematics, particularly non-commutative and fractal geometry. It will maintain and extend Australia's prominence in these subjects, providing excellent training and opportunities for young researchers. Given the wide range of applications of fractals, there is potential for future technological spin offs for Australia.
Natural resources and ecosystem services in productivity measurement. This project aims to understand sources of productivity growth through addressing theoretical and practical problems in the economics of natural resources and ecosystem services. It will study the valuation of non-renewable resources and ecosystem services, acknowledging their contributions to economic activity and the effect on national income from their depletion and degradation. It will develop approaches to incorporating n ....Natural resources and ecosystem services in productivity measurement. This project aims to understand sources of productivity growth through addressing theoretical and practical problems in the economics of natural resources and ecosystem services. It will study the valuation of non-renewable resources and ecosystem services, acknowledging their contributions to economic activity and the effect on national income from their depletion and degradation. It will develop approaches to incorporating natural resource depletion and degradation into productivity analysis with the aim of better informing environmental, innovation and industry policy.Read moreRead less
Inventories and the Business Cycle in Australia and the U.S. The project looks at the contribution that inventories make to business cycles in Australia and the U.S. It uses recent research by the chief investigator on measuring business cycles in order to explain how the presence of inventories in an economic system might influence activity in that system. It then adapts an existing model in the literature to quantify the role of inventories in the Australian and U.S business cycles.. It seeks ....Inventories and the Business Cycle in Australia and the U.S. The project looks at the contribution that inventories make to business cycles in Australia and the U.S. It uses recent research by the chief investigator on measuring business cycles in order to explain how the presence of inventories in an economic system might influence activity in that system. It then adapts an existing model in the literature to quantify the role of inventories in the Australian and U.S business cycles.. It seeks to answer a number of questions that have arisen in recent years over whether the business cycle is becoming longer owing to improved methods of inventory controlRead moreRead less
Can Electronic Point-of-Sale (POS) Data Improve the Australian Consumer Price Index? This project will investigate how new sources of data can be used to improve the accuracy of price indexes that are used in policy formation, such as the consumer price index. The adoption of bar-code labelling for products has provided statistical agencies with an information-rich source of 'scanner data' on prices and quantities of purchased goods. In collaboration with the Australian Bureau of Statistics, thi ....Can Electronic Point-of-Sale (POS) Data Improve the Australian Consumer Price Index? This project will investigate how new sources of data can be used to improve the accuracy of price indexes that are used in policy formation, such as the consumer price index. The adoption of bar-code labelling for products has provided statistical agencies with an information-rich source of 'scanner data' on prices and quantities of purchased goods. In collaboration with the Australian Bureau of Statistics, this project will develop mathematical and statistical methods for exploiting this new data source. The findings will contribute to the improvement of price indexes, and subsequently the many government policies that depend on these indexes.Read moreRead less
Scanner Data in the Consumer Price Index: How to expand and improve their use. The Consumer Price Index (CPI) is used in a variety of policy contexts, such as setting interest rates and determining the level of welfare payments, as well as by private industry for determining wages. The CPI is aggregate measure of price changes. It is typically constructed using survey data, which is a small sample of all the goods purchased. Electronic recording of sales, using scanned product bar codes, provide ....Scanner Data in the Consumer Price Index: How to expand and improve their use. The Consumer Price Index (CPI) is used in a variety of policy contexts, such as setting interest rates and determining the level of welfare payments, as well as by private industry for determining wages. The CPI is aggregate measure of price changes. It is typically constructed using survey data, which is a small sample of all the goods purchased. Electronic recording of sales, using scanned product bar codes, provides a huge amount of price and quantity information that potentially can be used to construct an improved CPI, and hence improved policies. The project includes the collaboration of the Australian Bureau of Statistics and the Central Bureau of Statistics (The Netherlands).Read moreRead less
Macroeconomic and Financial Modelling in an Era of Extremes. This project aims to develop methods to allow workhorse models in economics and finance to better reflect tail events--low probability extreme events, such as the Global Financial Crisis and the COVID-19 pandemic. It intends to address fundamental technical challenges in the estimation of such models, develop a coherent framework for counterfactual analysis of these models and propose methods to apply these models in a big-data environ ....Macroeconomic and Financial Modelling in an Era of Extremes. This project aims to develop methods to allow workhorse models in economics and finance to better reflect tail events--low probability extreme events, such as the Global Financial Crisis and the COVID-19 pandemic. It intends to address fundamental technical challenges in the estimation of such models, develop a coherent framework for counterfactual analysis of these models and propose methods to apply these models in a big-data environment. Expected outcomes include new insights into the transmission of tail risks in the global economic and financial system. This should provide significant benefits, including guidance to Australian and international policymakers charged with maintaining stability in the face of extreme events.Read moreRead less