Discovery Early Career Researcher Award - Grant ID: DE200101070
Funder
Australian Research Council
Funding Amount
$376,496.00
Summary
Consequences of Model Misspecification in Approximate Bayesian Computation. In almost any empirical application, the model the analyst is working with constitutes a misspecified description of the true process that has generated the data. While the method of Approximate Bayesian computation (ABC) is now a staple in the toolkit of the applied modeller, the impact of misspecification in ABC is unknown. This project aims to undertake a rigorous study into the behaviour of ABC under model misspecifi ....Consequences of Model Misspecification in Approximate Bayesian Computation. In almost any empirical application, the model the analyst is working with constitutes a misspecified description of the true process that has generated the data. While the method of Approximate Bayesian computation (ABC) is now a staple in the toolkit of the applied modeller, the impact of misspecification in ABC is unknown. This project aims to undertake a rigorous study into the behaviour of ABC under model misspecification. Expected outcomes include new theoretical results for ABC under misspecification and new methods capable of detecting/mitigating model misspecification. This project will provide significant benefits in all spheres where reliable, robust statistical inference methods are required in order to make reliable decisions.
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Discovery Early Career Researcher Award - Grant ID: DE230100029
Funder
Australian Research Council
Funding Amount
$345,197.00
Summary
Variational Inference for Intractable and Misspecified State Space Models. State space models (SSMs) are popularly used to model economic variables such as inflation and financial volatility. Variational inference is a technique that allows for fast implementation of SSMs, but whose properties are yet to be understood. This project aims to study the properties of variational inference for SSMs used in economics.
This research will develop new variational inference techniques to improve inferent ....Variational Inference for Intractable and Misspecified State Space Models. State space models (SSMs) are popularly used to model economic variables such as inflation and financial volatility. Variational inference is a technique that allows for fast implementation of SSMs, but whose properties are yet to be understood. This project aims to study the properties of variational inference for SSMs used in economics.
This research will develop new variational inference techniques to improve inferential and predictive accuracy from SSMs. An expected implication of this project is that it will expand the ability of economic institutions to employ larger SSMs, which will allow for more accurate models for economic variables. This will provide significant social benefits by leading to better informed economic policy.
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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
Solvability and universality in stochastic processes. Exactly solvable stochastic processes are an important area of mathematical research, with cross-disciplinary links to quantum physics, quantum algebras and probability theory. These processes can be used to model a variety of real-world phenomena such as crystal growth and polymers in random media. This project aims to significantly expand our knowledge of exactly solvable stochastic processes by extending them to new algebraic frameworks. A ....Solvability and universality in stochastic processes. Exactly solvable stochastic processes are an important area of mathematical research, with cross-disciplinary links to quantum physics, quantum algebras and probability theory. These processes can be used to model a variety of real-world phenomena such as crystal growth and polymers in random media. This project aims to significantly expand our knowledge of exactly solvable stochastic processes by extending them to new algebraic frameworks. Among the outcomes of the project, we expect to identify new probabilistic structures which go beyond the famous Gaussian universality class. These theoretical developments allow better prediction of randomly growing interfaces, which encompass a range of phenomena from tumour growth to forest fires.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
Discovery Early Career Researcher Award - Grant ID: DE210101264
Funder
Australian Research Council
Funding Amount
$342,346.00
Summary
Toroidal quantum groups, integrable models and applications. Modelling systems of quantum and classical mechanics usually relies on computationally expensive numerical methods. Such methods typically provide raw answers and give little insight. In contrast, a special class of modelling based on quantum integrability provides us with a variety of analytic tools thanks to connections with algebra, geometry and combinatorics. The project aims to study quantum integrability with the help of new exci ....Toroidal quantum groups, integrable models and applications. Modelling systems of quantum and classical mechanics usually relies on computationally expensive numerical methods. Such methods typically provide raw answers and give little insight. In contrast, a special class of modelling based on quantum integrability provides us with a variety of analytic tools thanks to connections with algebra, geometry and combinatorics. The project aims to study quantum integrability with the help of new exciting developments in toroidal quantum groups. The anticipated outcomes include constructions of new models, developing analytic methods and computer algebra packages. These results are expected to facilitate challenging computational problems in modelling of quantum and classical systems.Read moreRead less