Loss-based Bayesian Prediction. This project proposes a new paradigm for prediction. Using state-of-the-art computational methods, the project aims to produce accurate, fit for purpose, predictions which, by design, reduce the loss incurred when the prediction is inaccurate. Theoretical validation of the new predictive method, without reliance on knowledge of the correct statistical model, is an expected outcome, as is an extensive numerical assessment of its performance in empirical settings. T ....Loss-based Bayesian Prediction. This project proposes a new paradigm for prediction. Using state-of-the-art computational methods, the project aims to produce accurate, fit for purpose, predictions which, by design, reduce the loss incurred when the prediction is inaccurate. Theoretical validation of the new predictive method, without reliance on knowledge of the correct statistical model, is an expected outcome, as is an extensive numerical assessment of its performance in empirical settings. The new paradigm should produce significant benefits for all fields in which the consequences of predictive inaccuracy are severe. Problems that lead to substantial economic, financial or environmental loss if predictions are incorrect will be given particular attention.Read moreRead less
New methods for modelling complex trends in climate and energy time series. The project aims to contribute to Australian and international efforts on emission control by advancing the methods for quantifying the relationships between energy production, emission and climate, and assessing the real and financial risks associated with changing the ways in which economies produce and use energy. The project is interdisciplinary and expects to develop new knowledge in the areas of energy and climate ....New methods for modelling complex trends in climate and energy time series. The project aims to contribute to Australian and international efforts on emission control by advancing the methods for quantifying the relationships between energy production, emission and climate, and assessing the real and financial risks associated with changing the ways in which economies produce and use energy. The project is interdisciplinary and expects to develop new knowledge in the areas of energy and climate econometrics. The anticipated outcomes of this project are new methods for modelling variables with complex trends, and an innovative data-driven approach for learning from policy experiences of other countries. This should provide significant benefits by enabling evidence-based policy making in the era of climate change. Read moreRead less
Linking wave–sea ice feedbacks to rapid ice retreat. Antarctic sea ice extent has been in sharp decline since 2016, which is stressing the fragile Southern Ocean and Antarctic environments so vital to the global climate. This project aims to investigate a crucial candidate mechanism of sea ice loss by predicting rapid ice retreat in response to large Southern Ocean waves. New theory and modelling capabilities that account for wave–ice feedbacks will underpin the predictions, leveraging on recent ....Linking wave–sea ice feedbacks to rapid ice retreat. Antarctic sea ice extent has been in sharp decline since 2016, which is stressing the fragile Southern Ocean and Antarctic environments so vital to the global climate. This project aims to investigate a crucial candidate mechanism of sea ice loss by predicting rapid ice retreat in response to large Southern Ocean waves. New theory and modelling capabilities that account for wave–ice feedbacks will underpin the predictions, leveraging on recent research breakthroughs, including novel datasets derived from satellite and field observations. The outcomes are expected to quantify sea ice retreat due to ocean waves for the first time, with potentially major implications for coupled wave–sea ice modelling in climate studies.Read moreRead less
Transformative simulation techniques for complex polymer networks. The study of long chain polymers like DNA using computer simulations has uncovered exciting insights over many years. Generally these have been limited to simple topologies, interactions, and environments. This project aims to develop the next generation of simulation techniques to tackle a new frontier of polymer models, including those with complex topologies like stars, knots, and links, which have hitherto been inaccessible. ....Transformative simulation techniques for complex polymer networks. The study of long chain polymers like DNA using computer simulations has uncovered exciting insights over many years. Generally these have been limited to simple topologies, interactions, and environments. This project aims to develop the next generation of simulation techniques to tackle a new frontier of polymer models, including those with complex topologies like stars, knots, and links, which have hitherto been inaccessible. Expected outcomes include new simulation methods which harness modern computational clusters, leading to greater understanding of polymers with complex topologies and in complicated environments. Important elements of biological processes may be discovered, such as how polymer structure affects DNA transcription.Read moreRead less
Shuffle algebras and vertex models. Shuffle algebras are important new mathematical structures that offer a new approaches and techniques to solve outstanding open problems in a variety of branches of mathematics, including mathematical physics, algebraic geometry and combinatorics. This project proposes to find solutions to key open problems using connections between shuffle algebras and integrable lattice models. The expected outcomes include (i) a new framework of shuffle algebra techniques t ....Shuffle algebras and vertex models. Shuffle algebras are important new mathematical structures that offer a new approaches and techniques to solve outstanding open problems in a variety of branches of mathematics, including mathematical physics, algebraic geometry and combinatorics. This project proposes to find solutions to key open problems using connections between shuffle algebras and integrable lattice models. The expected outcomes include (i) a new framework of shuffle algebra techniques to solve challenging research problems in mathematical physics and statistical mechanics, (ii) practical and computationally feasible constructions of shuffle algebras using vertex models, (iii) solutions to unresolved spectral problems of open quantum systems.Read moreRead less
Matrix product multi-variable polynomials from quantum algebras. This project aims to expand the theory of polynomials and develop generalised polynomial families using connections to affine and toroidal algebras. Many combinatorial and computational problems in pure and applied mathematics as well as mathematical physics can be solved using polynomials in many variables, such as Macdonald polynomials. This project is anticipated to address the current difficulty of implementing symmetric and no ....Matrix product multi-variable polynomials from quantum algebras. This project aims to expand the theory of polynomials and develop generalised polynomial families using connections to affine and toroidal algebras. Many combinatorial and computational problems in pure and applied mathematics as well as mathematical physics can be solved using polynomials in many variables, such as Macdonald polynomials. This project is anticipated to address the current difficulty of implementing symmetric and non-symmetric polynomials in symbolic algebra packages by developing completely new algorithms. New understanding from the project is expected to facilitate challenging computational problems of measurable quantities in quantum systems.Read moreRead less
Expanding and linking random matrix theory. Fundamental to random matrix theory are certain universality laws, holding in scaling limits to infinite matrix size. A basic question is to quantify the rate of convergence to the universal laws. The analysis of data for the Riemann zeros from prime number theory, and of the spectral form factor probe of chaos in black hole physics, are immediate applications. An analysis involving integrable structures holding for finite matrix size and their asympt ....Expanding and linking random matrix theory. Fundamental to random matrix theory are certain universality laws, holding in scaling limits to infinite matrix size. A basic question is to quantify the rate of convergence to the universal laws. The analysis of data for the Riemann zeros from prime number theory, and of the spectral form factor probe of chaos in black hole physics, are immediate applications. An analysis involving integrable structures holding for finite matrix size and their asymptotics is proposed, allowing the rate to be quantified for a large class of model
ensembles, and providing predictions in the various applied settings. The broad project is to be networked with researchers in the Asia-Oceania region, with the aim of establishing leadership status for Australia.Read moreRead less
Robust methods for heteroscedastic regression models for time series. What is the variability of the exchange rate of the Euro to the Australian dollar? Can the use of the electrocardiogram of a patient be improved as a diagnostic tool for heart disease? A well-known limitation of the existing statistical methods for answering these types of questions is that a small proportion of extreme observations have the potential to lead to results that are more in agreement with the outliers than with bu ....Robust methods for heteroscedastic regression models for time series. What is the variability of the exchange rate of the Euro to the Australian dollar? Can the use of the electrocardiogram of a patient be improved as a diagnostic tool for heart disease? A well-known limitation of the existing statistical methods for answering these types of questions is that a small proportion of extreme observations have the potential to lead to results that are more in agreement with the outliers than with bulk of the data. As a consequence, the statistical analyses may lead to wrong conclusions. This project aims to develop new methodologies to solve this problem for a large class of studies. Applications to stock market risk, exchange rate, and diagnosis of heart diseases will illustrate the new methods.Read moreRead less
The weather-climate connection in Australian climate change. This project aims to uncover the key links in Australia's weather-climate connection by identifying the role weather features play in influencing the slowly varying climate and how changes in one might affect changes in the other. Better describing the two-way connection between weather and climate through an innovative combination of research techniques usually applied to only one of weather or climate will allow for a more insightful ....The weather-climate connection in Australian climate change. This project aims to uncover the key links in Australia's weather-climate connection by identifying the role weather features play in influencing the slowly varying climate and how changes in one might affect changes in the other. Better describing the two-way connection between weather and climate through an innovative combination of research techniques usually applied to only one of weather or climate will allow for a more insightful assessment of climate model quality. This assessment will support the identification of the most reliable climate models and, by using them, reduce uncertainties in future predictions. Improved predictions of climate in turn will enable better decision making in all sectors of society.Read moreRead less
Increasing the efficiency and interpretability of stepped wedge trials. Stepped wedge cluster randomised trials are increasingly being used to test interventions, across many disciplines. This project aims to develop highly efficient trial designs and new methods for the estimation of causally interpretable effects when adherence to interventions is not perfect. This project expects to generate new design types that reduce resources required to test interventions, and methods to understand how t ....Increasing the efficiency and interpretability of stepped wedge trials. Stepped wedge cluster randomised trials are increasingly being used to test interventions, across many disciplines. This project aims to develop highly efficient trial designs and new methods for the estimation of causally interpretable effects when adherence to interventions is not perfect. This project expects to generate new design types that reduce resources required to test interventions, and methods to understand how these interventions work. Expected outcomes include tools to help researchers develop cheaper and more appealing trials, tools to estimate causal effects, the methodology underpinning these tools, and new collaborations. This should provide significant benefits by allowing more interventions to be tested and understood.Read moreRead less