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
Inference for Hawkes processes with challenging data. The Hawkes processes are statistical models for the analysis of high-impact event sequences, such as bushfires, earthquakes, infectious diseases, and cyber attacks. When the times and/or marks are missing for some events or when the data is otherwise incomplete, it is challenging to fit these models and perform diagnostic checks on the fitted models. This project aims to develop novel statistical methods to fit these models in the presence of ....Inference for Hawkes processes with challenging data. The Hawkes processes are statistical models for the analysis of high-impact event sequences, such as bushfires, earthquakes, infectious diseases, and cyber attacks. When the times and/or marks are missing for some events or when the data is otherwise incomplete, it is challenging to fit these models and perform diagnostic checks on the fitted models. This project aims to develop novel statistical methods to fit these models in the presence of incomplete data and to check the goodness-of-fit of the fitted models. The expected outcomes include publications documenting these methods and software packages implementing them. The primary benefits include the advancement of statistical methodology and the training of junior research personnel. Read moreRead less
New methods for modelling real-world extremes. This project aims to develop new theory and methods for analysing and predicting extreme values observed in real-world processes. Many existing techniques are limited by convenient mathematical assumptions that commonly do not hold in practice: dependence at asymptotic levels, process stationarity, and that the observed data are direct measurements of the process of interest. As a result, using these techniques may produce undesirable results. Expec ....New methods for modelling real-world extremes. This project aims to develop new theory and methods for analysing and predicting extreme values observed in real-world processes. Many existing techniques are limited by convenient mathematical assumptions that commonly do not hold in practice: dependence at asymptotic levels, process stationarity, and that the observed data are direct measurements of the process of interest. As a result, using these techniques may produce undesirable results. Expected outcomes of this project include theoretically justified data analysis techniques that can accurately model extreme values seen in the real world. Project benefits include more realistic analyses of nationally important applications in climate, bushfire insurance risk, and anomaly detection.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE200100435
Funder
Australian Research Council
Funding Amount
$365,039.00
Summary
Modern statistical methods for complex multivariate longitudinal data. The project aims to develop novel approaches for the statistical analysis of large, complex multivariate longitudinal data, and apply them to two datasets to address scientific questions related to the drivers and consequences of poor physical and mental health in Australia, and the spatio-temporal evolution of species assemblages in the Southern Ocean. The project expects to develop new knowledge in the areas of statistical ....Modern statistical methods for complex multivariate longitudinal data. The project aims to develop novel approaches for the statistical analysis of large, complex multivariate longitudinal data, and apply them to two datasets to address scientific questions related to the drivers and consequences of poor physical and mental health in Australia, and the spatio-temporal evolution of species assemblages in the Southern Ocean. The project expects to develop new knowledge in the areas of statistical model building, model selection, and inference for multivariate longitudinal data. This will lead to a suite of modern methods and insights for computationally efficient, mathematically rigorous statistical data analysis that, when applied, should provide significant benefits to public health and ecology.Read moreRead less
Self-Interacting Random Walks. This project aims to study the growth properties of a class of self-interacting processes defined on Euclidean lattices. This project expects to determine whether a shape theorem holds for once-reinforced random walks, and establish conditions for their recurrence/transience. It also expects to obtain new and very precise estimates for the local time of simple random walks. Expected outcomes of this project include solving long-standing open problems in the field o ....Self-Interacting Random Walks. This project aims to study the growth properties of a class of self-interacting processes defined on Euclidean lattices. This project expects to determine whether a shape theorem holds for once-reinforced random walks, and establish conditions for their recurrence/transience. It also expects to obtain new and very precise estimates for the local time of simple random walks. Expected outcomes of this project include solving long-standing open problems in the field of reinforced random walks, and the development of novel methods for their study. This should provide significant benefits not only to the field of mathematics, but also to the myriad of applied disciplines where self-interacting processes are utilised.Read moreRead less
Perturbations in Complex Systems and Games. This project aims to: advance the perturbation theory of dynamic and stochastic games; further develop approximations of infinite dimensional linear programs by their finite dimensional counterparts, and by finding asymptotic limits of spaces of occupational measures, by solution of successive layers of fundamental equations; explain and quantify the "exceptionality" of instances of systems that are genuinely difficult to solve; and, capitalise on the ....Perturbations in Complex Systems and Games. This project aims to: advance the perturbation theory of dynamic and stochastic games; further develop approximations of infinite dimensional linear programs by their finite dimensional counterparts, and by finding asymptotic limits of spaces of occupational measures, by solution of successive layers of fundamental equations; explain and quantify the "exceptionality" of instances of systems that are genuinely difficult to solve; and, capitalise on the outstanding performance of our Snakes-and-Ladders Heuristic (SLH) for the solution of the Hamiltonian cycle problem to identify its "fixed complexity orbits" and generalise this notion to other NP-complete problems.Read moreRead less
Scalable and Robust Bayesian Inference for Implicit Statistical Models. This project aims to develop the next generation of efficient methods for fitting complex simulation-based statistical models to data. Practitioners and scientists are interested in such implicit models to enable discoveries, produce accurate predictions and inform decisions under uncertainty. However, the associated computational cost has restricted researchers to implicit models that must have a small number of parameters ....Scalable and Robust Bayesian Inference for Implicit Statistical Models. This project aims to develop the next generation of efficient methods for fitting complex simulation-based statistical models to data. Practitioners and scientists are interested in such implicit models to enable discoveries, produce accurate predictions and inform decisions under uncertainty. However, the associated computational cost has restricted researchers to implicit models that must have a small number of parameters and be well specified, impeding scientific progress. This project will develop new computational methods and algorithms for implicit models that scale to high dimensions and are robust to misspecification. Benefits will arise from the more routine use of implicit models in epidemiology, biology, ecology and other fields.Read moreRead less
Advances in Sequential Monte Carlo Methods for Complex Bayesian Models. This project aims to develop efficient statistical algorithms for parameter estimation of complex stochastic models that currently cannot be handled. Parameter estimation is an essential component of mathematical modelling for answering scientific questions and revealing new insights. Current parameter estimation methods can be inefficient and require too much user intervention. This project will develop novel Bayesian alg ....Advances in Sequential Monte Carlo Methods for Complex Bayesian Models. This project aims to develop efficient statistical algorithms for parameter estimation of complex stochastic models that currently cannot be handled. Parameter estimation is an essential component of mathematical modelling for answering scientific questions and revealing new insights. Current parameter estimation methods can be inefficient and require too much user intervention. This project will develop novel Bayesian algorithms that are optimally automated and efficient by exploiting ever-improving parallel computing devices. The new methods will allow practitioners to process realistic models, enabling new scientific discoveries in a wide range of disciplines such as biology, ecology, agriculture, hydrology and finance.Read moreRead less
Statistical methods for quantifying variation in spatiotemporal areal data. This project aims to develop new statistical methods for extracting insights into spatial and temporal variation in areal data. These tools will extend the Australian Cancer Atlas which provides small area estimates for 20 cancers across Australia. The project is significant because it will allow government and other organisations to reap dividends from investment in collecting spatial information and it will enable mode ....Statistical methods for quantifying variation in spatiotemporal areal data. This project aims to develop new statistical methods for extracting insights into spatial and temporal variation in areal data. These tools will extend the Australian Cancer Atlas which provides small area estimates for 20 cancers across Australia. The project is significant because it will allow government and other organisations to reap dividends from investment in collecting spatial information and it will enable modelled small-area estimates to be released without compromising confidentiality. The expected outcomes include new statistical knowledge and new insights into cancer. The results will benefit the many disciplines, managers and policy makers that make decisions based on geographic data mapped over space and time. 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