High Predictive Performance Models via Semi-Parametric Survival Regression. This project will develop novel statistical models for high prediction performance. When applied to help doctor to treat patients, these models allow the users to include gene or other biomarkers for predicting effectiveness of a treatment. When applied to risk management in finance, these models are capable to include an organization's or individual's ongoing finance status to predict, for example, the probability of or ....High Predictive Performance Models via Semi-Parametric Survival Regression. This project will develop novel statistical models for high prediction performance. When applied to help doctor to treat patients, these models allow the users to include gene or other biomarkers for predicting effectiveness of a treatment. When applied to risk management in finance, these models are capable to include an organization's or individual's ongoing finance status to predict, for example, the probability of or time to loan default. Innovative computational methods will be developed for fitting these models. Compared to traditional prediction method, this approach allows greater flexibility while being superior in terms of statistical accuracy and bias. Extensive analyses of healthcare data from diverse fields will be undertaken.Read moreRead less
Stochastic majorization--minimization algorithms for data science. The changing nature of acquisition and storage data has made the process of drawing inference infeasible with traditional statistical and machine learning methods. Modern data are often acquired in real time, in an incremental nature, and are often available in too large a volume to process on conventional machinery. The project proposes to study the family of stochastic majorisation-minimisation algorithms for computation of inf ....Stochastic majorization--minimization algorithms for data science. The changing nature of acquisition and storage data has made the process of drawing inference infeasible with traditional statistical and machine learning methods. Modern data are often acquired in real time, in an incremental nature, and are often available in too large a volume to process on conventional machinery. The project proposes to study the family of stochastic majorisation-minimisation algorithms for computation of inferential quantities in an incremental manner. The proposed stochastic algorithms encompass and extend upon a wide variety of current algorithmic frameworks for fitting statistical and machine learning models, and can be used to produce feasible and practical algorithms for complex models, both current and future.
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Computational methods for population-size-dependent branching processes. Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project ....Computational methods for population-size-dependent branching processes. Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project aims to develop novel and effective algorithmic techniques and statistical methods for a class of branching processes with dependences. We will use these results to study significant problems in the conservation of endangered island bird populations in Oceania, and to help inform their conservation management.Read moreRead less
New universality in stochastic systems. This project aims to uncover new analyses and effects in the complex behaviour of non-linear systems with random noise. Many systems originate near an unstable equilibrium. This project will develop a new mathematical theory that establishes a universality in the way the long term effect of noise expresses itself as random initial conditions in the dynamics. It will fill gaps in Mathematics and make refinements to existing fundamental scientific laws by in ....New universality in stochastic systems. This project aims to uncover new analyses and effects in the complex behaviour of non-linear systems with random noise. Many systems originate near an unstable equilibrium. This project will develop a new mathematical theory that establishes a universality in the way the long term effect of noise expresses itself as random initial conditions in the dynamics. It will fill gaps in Mathematics and make refinements to existing fundamental scientific laws by including random initial conditions as predicted by our theory. This will advance our understanding of complex systems subjected to noise and will provide significant benefits in the scientific discoveries in Biology, Ecology, Physics and other Sciences where such systems are frequently met.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
Random fields: non-Gaussian stochastic models and approximation schemes. The project aims to address important problems in the theory and statistics of stochastic processes and develop new methodology for their applications. This project expects to generate new knowledge about stochastic processes defined on multidimensional spaces and surfaces that are used in spatio-temporal data modelling. Main anticipated outcomes include
- developing approximation schemes for new complex data and investi ....Random fields: non-Gaussian stochastic models and approximation schemes. The project aims to address important problems in the theory and statistics of stochastic processes and develop new methodology for their applications. This project expects to generate new knowledge about stochastic processes defined on multidimensional spaces and surfaces that are used in spatio-temporal data modelling. Main anticipated outcomes include
- developing approximation schemes for new complex data and investigating their accuracy and reliability;
- studying nonlinear statistics and transformations of these data;
- providing new tools to investigate complex real data, in particular, in cosmology and embryology.
The results should provide significant benefits for optimal modelling and analysis of high resolution big data.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
Visualisation of multidimensional physics data. This project aims to link multi-parameter models used in physics to explore experimental data, and statistical tools for multivariate analysis and visualisation. It addresses an important gap in the understanding of phenomenological physics analyses containing many simultaneously important parameters. This is expected to improve the understanding of results in multi-parameter models.
Discovery Early Career Researcher Award - Grant ID: DE190101326
Funder
Australian Research Council
Funding Amount
$391,546.00
Summary
Statistical methods for modelling the pathways between cause and effect. This project aims to develop new biostatistical methods for addressing complex analytic questions that arise in studies of the causes of health, social, educational and other outcomes in the course of human life. These questions concern the pathways that explain how intermediate factors contribute to a statistical relationship between a probable cause of a later outcome. Mathematical and statistical innovation is needed to ....Statistical methods for modelling the pathways between cause and effect. This project aims to develop new biostatistical methods for addressing complex analytic questions that arise in studies of the causes of health, social, educational and other outcomes in the course of human life. These questions concern the pathways that explain how intermediate factors contribute to a statistical relationship between a probable cause of a later outcome. Mathematical and statistical innovation is needed to address them. The expected outcomes include a suite of novel methods designed to evaluate the impact of intervening to modify causal pathways, while also accommodating common complexities of data such as incompleteness. This project should provide major benefits to studies in public health, social sciences and economics.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE210101352
Funder
Australian Research Council
Funding Amount
$330,000.00
Summary
Inverting the Signature Transform for Rough Paths and Random Processes. The signature transform provides an effective summary of the essential information encoded in multidimensional paths that are highly oscillatory and involve complicated randomness. The main goal of this project is to develop new algorithmic methods to reconstruct rough paths and random processes from the signature transform at various quantitative levels. This project expects to make theoretical breakthrough on the significa ....Inverting the Signature Transform for Rough Paths and Random Processes. The signature transform provides an effective summary of the essential information encoded in multidimensional paths that are highly oscillatory and involve complicated randomness. The main goal of this project is to develop new algorithmic methods to reconstruct rough paths and random processes from the signature transform at various quantitative levels. This project expects to make theoretical breakthrough on the significant open problem of signature inversion, thereby advancing knowledge in the areas of rough path theory and stochastic analysis. The newly developed methods will be utilised in combination with the emerging signature-based approach to study important problems in financial data analysis and visual speech recognition.
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