Discovery Early Career Researcher Award - Grant ID: DE240101190
Funder
Australian Research Council
Funding Amount
$451,000.00
Summary
Innovating and Validating Scalable Monte Carlo Methods. This project aims to develop innovative scalable Monte Carlo methods for statistical analysis in the presence of big data or complex mathematical models. Existing approaches to scalable Monte Carlo are only approximate, and their inaccuracies are difficult to quantify. This can have a detrimental impact on data-based decision making. The expected outcomes of this project are scalable Monte Carlo methods that are more accurate, fast and capa ....Innovating and Validating Scalable Monte Carlo Methods. This project aims to develop innovative scalable Monte Carlo methods for statistical analysis in the presence of big data or complex mathematical models. Existing approaches to scalable Monte Carlo are only approximate, and their inaccuracies are difficult to quantify. This can have a detrimental impact on data-based decision making. The expected outcomes of this project are scalable Monte Carlo methods that are more accurate, fast and capable of quantifying inaccuracies. Scientists and decision-makers will benefit from the ability to obtain timely, reliable insights for challenging applications.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE200101467
Funder
Australian Research Council
Funding Amount
$419,778.00
Summary
The geometric structure of spatial noise. Spatial noise is ubiquitous in nature and science: as interference in medical imaging, in oceanography, in the modelling of telecommunication networks etc. Despite this diversity of sources, spatial noise can be studied in a unified way by considering mathematical models that capture its essential features. This project aims to study spatial noise by analysing its geometric structure, for instance by considering the number of contour lines of the noise, ....The geometric structure of spatial noise. Spatial noise is ubiquitous in nature and science: as interference in medical imaging, in oceanography, in the modelling of telecommunication networks etc. Despite this diversity of sources, spatial noise can be studied in a unified way by considering mathematical models that capture its essential features. This project aims to study spatial noise by analysing its geometric structure, for instance by considering the number of contour lines of the noise, and the way these lines connect different regions of space. The project further aims to apply this analysis to construct statistical tests that can distinguish different classes of spatial noise, with potential applications across all of the disciplines mentioned above.Read moreRead less
Time consistency, risk-mitigation and partially observable systems. This project aims to find optimal decision rules that mitigate risk in a time consistent manner for partially observable systems. Many problems in conservation management and engineering systems are dependent on random environments and entail risk of failure. The challenge of consistently minimising such a risk while achieving satisfactory and sustainable resource consumption is considerable. This project aims to develop analyti ....Time consistency, risk-mitigation and partially observable systems. This project aims to find optimal decision rules that mitigate risk in a time consistent manner for partially observable systems. Many problems in conservation management and engineering systems are dependent on random environments and entail risk of failure. The challenge of consistently minimising such a risk while achieving satisfactory and sustainable resource consumption is considerable. This project aims to develop analytical and numerical methods for optimal control in such scenarios. These methods will have application to fishery management, communication networks, power systems and social resource allocation scenarios.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
Stochastic majorization--minimization algorithms for data science. The changing nature of acquisition and storage data has made the process of drawing inference infeasible with traditional statistical and machine learning methods. Modern data are often acquired in real time, in an incremental nature, and are often available in too large a volume to process on conventional machinery. The project proposes to study the family of stochastic majorisation-minimisation algorithms for computation of inf ....Stochastic majorization--minimization algorithms for data science. The changing nature of acquisition and storage data has made the process of drawing inference infeasible with traditional statistical and machine learning methods. Modern data are often acquired in real time, in an incremental nature, and are often available in too large a volume to process on conventional machinery. The project proposes to study the family of stochastic majorisation-minimisation algorithms for computation of inferential quantities in an incremental manner. The proposed stochastic algorithms encompass and extend upon a wide variety of current algorithmic frameworks for fitting statistical and machine learning models, and can be used to produce feasible and practical algorithms for complex models, both current and future.
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Feature Learning for High-dimensional Functional Time Series. This project aims to develop new methods and theories for common features on high-dimensional functional time series observed in empirical applications. The significance includes addressing a key gap in adaptive and efficient feature learning, improving forecasting accuracy and understanding forecasting-driven factors comprehensively for empirical data. Expected outcomes involve advances in big data theory and easy-to-implement algori ....Feature Learning for High-dimensional Functional Time Series. This project aims to develop new methods and theories for common features on high-dimensional functional time series observed in empirical applications. The significance includes addressing a key gap in adaptive and efficient feature learning, improving forecasting accuracy and understanding forecasting-driven factors comprehensively for empirical data. Expected outcomes involve advances in big data theory and easy-to-implement algorithms for applied researchers. This project benefits not only advanced manufacturing by finding optimal stopping time for wood panel compression, but also superior forecasting for mortality in demography, climate data in environmental science, asset returns in finance, and electricity consumption in economics. Read moreRead less
Creating new stochastic models to understand the evolution of gene families. This project aims to extend stochastic modelling techniques in order to develop mathematically rigorous and biologically relevant models for the evolution of gene families. The project expects to model evolutionary processes such as gene retention, duplication and loss, and the generation of new gene functions. The duplication and subsequent re-purposing of genes is thought to be a key mechanism for generating evolution ....Creating new stochastic models to understand the evolution of gene families. This project aims to extend stochastic modelling techniques in order to develop mathematically rigorous and biologically relevant models for the evolution of gene families. The project expects to model evolutionary processes such as gene retention, duplication and loss, and the generation of new gene functions. The duplication and subsequent re-purposing of genes is thought to be a key mechanism for generating evolutionary novelty. By applying these models to genome data, the project expects to be able to quantify the importance of these different evolutionary mechanisms. The project will strengthen collaborative links between researchers in stochastic modelling and molecular evolutionary biology.Read moreRead less
Can green investors drive the transition to a low emissions economy? The project aims to develop a game-theoretical approach to model the impact of climate change on financial markets by studying the interactions between the government, companies and investors. Expected outcomes include novel solution concepts for stochastic games with heterogeneous beliefs, asymmetric information, and model uncertainty, as well as optimal investment and production strategies under climate driven economic transi ....Can green investors drive the transition to a low emissions economy? The project aims to develop a game-theoretical approach to model the impact of climate change on financial markets by studying the interactions between the government, companies and investors. Expected outcomes include novel solution concepts for stochastic games with heterogeneous beliefs, asymmetric information, and model uncertainty, as well as optimal investment and production strategies under climate driven economic transitions. Results will be used to validate and improve the recently launched Australian based climate transition index. The project should yield significant benefits for the financial industry and investors by providing novel insights into financial risks during the transition to a low emissions economy.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE200100896
Funder
Australian Research Council
Funding Amount
$427,008.00
Summary
How to beat model uncertainty with more information. Experience of the 2008 financial crisis exposed a weakness in our over-reliance on mathematical models. The main aim of this project is to develop mathematical tools to investigate the role of information in reducing model uncertainty. The project will undertake pressing research in robust finance, which is now one of the most active and dynamic topics in financial mathematics. It expects to quantify the value of information under uncertainty ....How to beat model uncertainty with more information. Experience of the 2008 financial crisis exposed a weakness in our over-reliance on mathematical models. The main aim of this project is to develop mathematical tools to investigate the role of information in reducing model uncertainty. The project will undertake pressing research in robust finance, which is now one of the most active and dynamic topics in financial mathematics. It expects to quantify the value of information under uncertainty in mathematical modelling. It will generate new knowledge in probability theory and stochastic processes providing a significant mathematical contribution in its own right.Read moreRead less
Advanced mathematical models and methods for a randomly-varying world. This project aims to develop advanced stochastic models and novel techniques, to analytically obtain performance measures and to efficiently simulate the time evolution. This project also plans to apply new models and methods to address important problems in ecology and epidemiology. The outputs of this project will advance knowledge in mathematics as well as in the intended application areas, including ultimately in improved ....Advanced mathematical models and methods for a randomly-varying world. This project aims to develop advanced stochastic models and novel techniques, to analytically obtain performance measures and to efficiently simulate the time evolution. This project also plans to apply new models and methods to address important problems in ecology and epidemiology. The outputs of this project will advance knowledge in mathematics as well as in the intended application areas, including ultimately in improved understanding, modelling, and tracking of the spread of diseases.Read moreRead less