New Methods in Theory and Cosmic Applications of Spherical Random Fields. This project aims to investigate and model spherical random fields which are described as solutions of stochastic differential equations on a sphere or a ball. The project plans to study properties and develop spectral analysis of these solutions. It then plans to use the obtained theoretical results to construct new methods for numerical approximation and statistical estimation of these random fields. In particular, it pl ....New Methods in Theory and Cosmic Applications of Spherical Random Fields. This project aims to investigate and model spherical random fields which are described as solutions of stochastic differential equations on a sphere or a ball. The project plans to study properties and develop spectral analysis of these solutions. It then plans to use the obtained theoretical results to construct new methods for numerical approximation and statistical estimation of these random fields. In particular, it plans to develop novel asymptotic and statistical methodology for tensor random fields. The project will apply the results to model and analyse cosmic microwave background data. Expected outcomes will improve the accuracy in determining cosmological parameters and provide novel tools for better understanding of the universe during its early stages.Read moreRead less
The mathematics of novel magnetic memory materials. Magnetic memories are the world’s principal device for storing information. The next generation will have greatly increased access speed and data-storage capacity. This project will develop the mathematical theory of these new magnetic memory materials, a crucial first step in understanding and being able to fine-tune their properties.
ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights. In today's world, massive amounts of data in a variety of forms are collected daily from a multitude of sources. Many of the resulting data sets have the potential to make vital contributions to society, business and government, as well as impact on international developments, but are so large or complex that they are difficult to process and analyse using traditional tools. The aim of this ....ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights. In today's world, massive amounts of data in a variety of forms are collected daily from a multitude of sources. Many of the resulting data sets have the potential to make vital contributions to society, business and government, as well as impact on international developments, but are so large or complex that they are difficult to process and analyse using traditional tools. The aim of this Centre is to create innovative mathematical and statistical models that can uncover the knowledge concealed within the size and complexity of these big data sets, with a focus on using the models to deliver insight into problems vital to the Centre's Collaborative Domains: Healthy People, Sustainable Environments and Prosperous Societies.Read moreRead less
Classification of Microarray Gene-Expression Data. The broad aim is to provide statistical methodology for the classification of microarray gene-expression data. Microarrays are part of a new biotechnology that allows the monitoring of expression levels for thousands of genes simultaneously. The explosion in microarrays has produced massive quantities of data that require new statistical techniques for analysis in order to exploit their enormous scientific potential. One of the main uses of ....Classification of Microarray Gene-Expression Data. The broad aim is to provide statistical methodology for the classification of microarray gene-expression data. Microarrays are part of a new biotechnology that allows the monitoring of expression levels for thousands of genes simultaneously. The explosion in microarrays has produced massive quantities of data that require new statistical techniques for analysis in order to exploit their enormous scientific potential. One of the main uses of the methodology to be developed is to expedite the discovery of new subclasses of diseases. Another is to provide prediction rules for the diagnosis and treatment of diseases.Read moreRead less
New Directions in Bayesian Statistics: formulation, computation and application to exemplar challenges. Bayesian statistics is a fundamental statistical and machine learning approach for density estimation, data analysis and inference. However, there remain open questions regarding the formulation of the model, the likelihood and priors, and efficient computation. This project proposes new approaches that address these issues, and applies them to two exemplar challenges: the impact of climate ch ....New Directions in Bayesian Statistics: formulation, computation and application to exemplar challenges. Bayesian statistics is a fundamental statistical and machine learning approach for density estimation, data analysis and inference. However, there remain open questions regarding the formulation of the model, the likelihood and priors, and efficient computation. This project proposes new approaches that address these issues, and applies them to two exemplar challenges: the impact of climate change on the Great Barrier Reef and better understanding neurological diseases related aging, in particular Parkinson's Disease. Read moreRead less
Generalised Degrees of Freedom and Probabilistic Regularisation. This project intends to develop novel statistical tools for more accurate prediction by taking account of model complexity and uncertainties associated with the fitting procedure. The project also plans to develop a novel shrinkage approach via new penalty functions to avoid over-fitting and asymptotic properties. The key applications may include genetic studies where the number of predictors is large and biological experiments whe ....Generalised Degrees of Freedom and Probabilistic Regularisation. This project intends to develop novel statistical tools for more accurate prediction by taking account of model complexity and uncertainties associated with the fitting procedure. The project also plans to develop a novel shrinkage approach via new penalty functions to avoid over-fitting and asymptotic properties. The key applications may include genetic studies where the number of predictors is large and biological experiments where multivariate and temporal data are often collected – for example economical breeding in animal and fish farming and more effectively detecting the genes of interest in genetic studies on human, animals and plants.Read moreRead less
Robust inferences for analysis of longitudinal data. This project will develop novel statistical tools. Outcomes of this project will enable more reliable data analysis and more cost effective designs in environmental and biological studies.
Precision ecology: the modern era of designed experiments in plant ecology. This project aims to develop the field of precision ecology, forging a new era of designed experiments where sampling is informed by research questions and what is known about the ecological process being studied. Through the development of novel statistical methods, new experiments globally will be designed to answer important ecological questions including what influence abiotic and biotic factors have on plant commun ....Precision ecology: the modern era of designed experiments in plant ecology. This project aims to develop the field of precision ecology, forging a new era of designed experiments where sampling is informed by research questions and what is known about the ecological process being studied. Through the development of novel statistical methods, new experiments globally will be designed to answer important ecological questions including what influence abiotic and biotic factors have on plant communities over time and different spatial scales. Expected outcomes include new methods and tools that will modernise how future experiments will be conducted in plant ecology. This will provide significant transdisciplinary benefits including new statistical methods that target scientific discovery in ecological studies.Read moreRead less
Cross-Entropy Methods in Complex Biological Systems. The Cross-Entropy method provides a powerful new way to find superior solutions to complicated optimisation problems in biology, ranging from better design and implementation of medical treatments to an increased understanding of complex ecosystems.
Applications of Bayesian methods in Genomics and Comparative Genomics. Bayesian statistics provides a unified and versatile approach to problems of data analysis, inference and hypothesis testing. This project will involve the application of Bayesian methods to four topics of commercial and scientific importance in the fields of Genomics and Comparative Genomics. The four topics are: data analysis for a novel DNA sequencing technology, investigating genomic structure using multiple change-point ....Applications of Bayesian methods in Genomics and Comparative Genomics. Bayesian statistics provides a unified and versatile approach to problems of data analysis, inference and hypothesis testing. This project will involve the application of Bayesian methods to four topics of commercial and scientific importance in the fields of Genomics and Comparative Genomics. The four topics are: data analysis for a novel DNA sequencing technology, investigating genomic structure using multiple change-point analysis, phlogenetic inference with multiple genes and detection of incongruent phylogenies. The overall goal of the project is to advance understanding of the structure, function and evolution of genomes.Read moreRead less