Guiding principles and guardrails for genetic association studies. This project aims to investigate deep connections between genetic structure (population genetic processes, linkage disequilibrium and population structure) and the ability to statistically detect genetic variants responsible for variation in traits. The project expects to generate new knowledge in the areas of statistics, mathematics and biology through an innovative, multidisciplinary approach that synthesises and extends founda ....Guiding principles and guardrails for genetic association studies. This project aims to investigate deep connections between genetic structure (population genetic processes, linkage disequilibrium and population structure) and the ability to statistically detect genetic variants responsible for variation in traits. The project expects to generate new knowledge in the areas of statistics, mathematics and biology through an innovative, multidisciplinary approach that synthesises and extends foundational disciplinary results. Expected outcomes of this project include principles and methodology that underpin future genetic association studies by supplying a framework for interpreting results. This should provide significant benefits by reducing false conclusions and their associated costs.Read moreRead less
Novel statistical methods for data with non-Euclidean geometric structure. This project aims to develop new flexible regression models and classification algorithms, along with robust and efficient inference methods, applicable to a wide range of non-Euclidean data types which arise in many fields of science, business and technology. There are serious flaws with currently available methods of analysis for non-Euclidean data. This project expects to transform such analyses by providing new quanti ....Novel statistical methods for data with non-Euclidean geometric structure. This project aims to develop new flexible regression models and classification algorithms, along with robust and efficient inference methods, applicable to a wide range of non-Euclidean data types which arise in many fields of science, business and technology. There are serious flaws with currently available methods of analysis for non-Euclidean data. This project expects to transform such analyses by providing new quantitative tools within a unifying framework. The anticipated project outcomes will be of mathematical interest and valuable in applications such as finance (predicting Australian stock returns); modelling electroencephalography data; Australian geochemical data, relating to sediments; and Australian X-ray tumour image data. Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE180100220
Funder
Australian Research Council
Funding Amount
$369,075.00
Summary
Statistics for manifold-valued data. This project aims to develop, and then implement, a new suite of fully flexible, interpretable and tractable models for manifold-valued data, along with robust and accurate estimation techniques for their parameters. Multivariate data with complicated constraints, such as manifold-valued data, is frequently encountered in the physical, biological and medical sciences, however it is difficult to define tractable statistical models and estimate their parameters ....Statistics for manifold-valued data. This project aims to develop, and then implement, a new suite of fully flexible, interpretable and tractable models for manifold-valued data, along with robust and accurate estimation techniques for their parameters. Multivariate data with complicated constraints, such as manifold-valued data, is frequently encountered in the physical, biological and medical sciences, however it is difficult to define tractable statistical models and estimate their parameters due to the curvature and nonlinear geometry of the sample space. The outcomes of the project are of direct mathematical interest as well as having significant interest to science and business disciplines where manifold-valued data is commonly observed.Read moreRead less
Novel techniques for statistical and mathematical analyses of sequence data. Algorithms will be developed for analysing and comparing the sequences of DNA letters and amino acids constantly being generated in massive quantities by biological research. The novel approach taken is based on the statistical frequency of occurrence of short words and is designed specifically for situations where current methods fail.
Bayesian inversion and computation applied to atmospheric flux fields. This project aims to make use of unprecedented sources of measurements, from remote sensing and in situ data, to estimate the sources and sinks of greenhouse gases. An overabundance of greenhouse gases in Earth's atmosphere is arguably the most serious long-term threat to the planet's ecosystems. This project will combine measurement uncertainties, process uncertainties in the physical transport models, and any parameter unce ....Bayesian inversion and computation applied to atmospheric flux fields. This project aims to make use of unprecedented sources of measurements, from remote sensing and in situ data, to estimate the sources and sinks of greenhouse gases. An overabundance of greenhouse gases in Earth's atmosphere is arguably the most serious long-term threat to the planet's ecosystems. This project will combine measurement uncertainties, process uncertainties in the physical transport models, and any parameter uncertainties, to provide reliable uncertainty quantification for the estimates. This will be achieved with new Bayesian spatio-temporal inversions and big-data computational strategies. The resulting statistical inferences on greenhouse-gas flux fields will enable the development of critical mitigation strategies. These new statistical inferences will be a valuable resource to policy-makers worldwide, who are assessing progress towards global commitments. Further, the final product may assist in developing cost-effective mitigation strategies in the presence of uncertainty.Read moreRead less
Canonical quantisation for classical integrable equations. This project is in the area of fundamental, enabling science. Integrable systems, both classical and quantum, arise as certain classes of dynamical universality in various problems of pure and applied mathematics and in physics. The project will significantly deepen our understanding of cross-relations between geometry and integrable systems.
The stability and predictability of the Southern Hemisphere coupled ocean-atmosphere climate system. Our ability to adapt to and manage the effects of a changing climate is limited by our understanding of the ocean's response to changes in the atmospheric circulation. This project will establish the basis for the predictability of the climate system and provide state-of-the-art forecasts for climate adaptation.
Free parafermions: a challenge for non-Hermitian physics. This project aims to calculate and understand the physical properties of free parafermions. Parafermions have attracted interest in topological schemes for quantum computation because they are computationally more powerful than Majorana fermions. The core of this project is a fundamental model of free parafermions, which has been shown to exhibit unexplained puzzling properties. The project outcomes include an in-depth understanding of th ....Free parafermions: a challenge for non-Hermitian physics. This project aims to calculate and understand the physical properties of free parafermions. Parafermions have attracted interest in topological schemes for quantum computation because they are computationally more powerful than Majorana fermions. The core of this project is a fundamental model of free parafermions, which has been shown to exhibit unexplained puzzling properties. The project outcomes include an in-depth understanding of this model by taking the non-Hermitian features into account, establishing a connection with open quantum systems. Non-Hermitian systems are also of increasing relevance in physics, especially in quantum optics. The project also aims to contribute to training researchers in the mathematical sciences.
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Rogue waves in realistic situations. Rapid progress in rogue wave research internationally requires the further development of an accurate theory of extreme waves in deep water and in optical fibers. Such progress is a necessity for our ability to predict their appearance in the ocean or their use in optics. This project will enhance the modelling of extreme waves by taking into account higher order effects such as third order dispersion, self-steepening and time delayed response, as well as dis ....Rogue waves in realistic situations. Rapid progress in rogue wave research internationally requires the further development of an accurate theory of extreme waves in deep water and in optical fibers. Such progress is a necessity for our ability to predict their appearance in the ocean or their use in optics. This project will enhance the modelling of extreme waves by taking into account higher order effects such as third order dispersion, self-steepening and time delayed response, as well as dissipative and higher order nonlinear terms. These are essential for a precise description of both giant waves in the ocean and strong pulses in optics. Read moreRead less
Evolutionary analyses of short-read sequences from pooled samples. This project aims to provide biologists with a means of making sound, statistical inferences about evolution by using next-generation data from mixed samples. When biologists make statements about history, they use evolutionary trees, frequently reconstructed from the genetic data of many individuals. Next-generation sequencing provides large amounts of genetic data at low cost, but biologists have difficulty using these data for ....Evolutionary analyses of short-read sequences from pooled samples. This project aims to provide biologists with a means of making sound, statistical inferences about evolution by using next-generation data from mixed samples. When biologists make statements about history, they use evolutionary trees, frequently reconstructed from the genetic data of many individuals. Next-generation sequencing provides large amounts of genetic data at low cost, but biologists have difficulty using these data for evolutionary research, particularly when they sample mixtures of DNA from many individuals. The anticipated value of this project is that it allows evolutionary biologists to capitalise on the benefits of next-generation sequencing, without sacrificing their ability to make reliable inferences about history.Read moreRead less