Frontiers in inference about risk. The project aims to develop new methods for robust risk evaluation and minimisation under various constraints and scenarios. Risk evaluation, estimation and prediction using past data is a central activity in diverse areas such as finance, insurance, superannuation and environmental regulation. The project aims to propose and solve innovatively robust risk optimisation problems under constraints, taking into account the time dynamics. Applications include risk ....Frontiers in inference about risk. The project aims to develop new methods for robust risk evaluation and minimisation under various constraints and scenarios. Risk evaluation, estimation and prediction using past data is a central activity in diverse areas such as finance, insurance, superannuation and environmental regulation. The project aims to propose and solve innovatively robust risk optimisation problems under constraints, taking into account the time dynamics. Applications include risk management around natural catastrophes and long-term asset investment of pension funds. The solutions and outcomes are expected to deliver optimal resource allocation proposals and better management of risk exposure in practice.Read moreRead less
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
Statistical methodology for events on a network, with application to road safety. This project develops new methods to analyse road traffic accident rates, aiming to identify accident black spots and to develop an evidence base for future road design and road safety management. These methods can be applied to other types of events on a network of roads, railways, rivers, electrical wires, communication networks or airline routes.
Discovery Early Career Researcher Award - Grant ID: DE160100741
Funder
Australian Research Council
Funding Amount
$382,274.00
Summary
Tractable Bayesian algorithms for intractable Bayesian problems. This project seeks to develop computationally efficient and scalable Bayesian algorithms to estimate the parameters of complex models and ensure inferences drawn from the models can be trusted. Bayesian parameter estimation and model validation procedures are currently computationally intractable for many complex models of interest in science and technology. These include biological processes such as the efficacy of heart disease, ....Tractable Bayesian algorithms for intractable Bayesian problems. This project seeks to develop computationally efficient and scalable Bayesian algorithms to estimate the parameters of complex models and ensure inferences drawn from the models can be trusted. Bayesian parameter estimation and model validation procedures are currently computationally intractable for many complex models of interest in science and technology. These include biological processes such as the efficacy of heart disease, wound healing and skin cancer treatments. Potential outcomes of the project include new algorithms to significantly economise computations and improved understanding of the mechanisms of experimental data generation. Improved models of wound healing, skin cancer growth and heart physiology supported by these algorithms could improve population health.Read moreRead less
Phase transitions in stochastic systems. This project aims to understand models of physical and biological phenomena in the presence of uncertainty/randomness. Such models often exhibit phase transitions if a variable defining the model is modified. For example, a population explosion can occur if the average number of offspring per individual is larger than one, while macroscopic defects can occur in a material if the density of microscopic defects is larger than some threshold. This research c ....Phase transitions in stochastic systems. This project aims to understand models of physical and biological phenomena in the presence of uncertainty/randomness. Such models often exhibit phase transitions if a variable defining the model is modified. For example, a population explosion can occur if the average number of offspring per individual is larger than one, while macroscopic defects can occur in a material if the density of microscopic defects is larger than some threshold. This research could lead to strategies for directing physical and biological systems towards preferred states or phases, and better prediction of adverse events such as fracturing of Antarctic sea ice.Read moreRead less
Advanced matrix-analytic methods with applications. Over the last twenty-five years, matrix-analytic methods have proved to be very successful in formulating and analysing certain classes of stochastic models. Motivated by applications, this project will investigate more advanced matrix-analytic methods than have hitherto been studied.
Discovery Early Career Researcher Award - Grant ID: DE160100999
Funder
Australian Research Council
Funding Amount
$295,020.00
Summary
Applying forward-backward stochastic differential equations to optimisation. This project intends to develop new ways to solve optimisation problems that are currently difficult to solve because of their complexity and size. In particular, forward–backward stochastic differential equations (FBSDEs) are a new technique that is showing ways to solve problems for which there is yet to be a solution. This project's focus will be on problems that cannot use existing software because the decision-maki ....Applying forward-backward stochastic differential equations to optimisation. This project intends to develop new ways to solve optimisation problems that are currently difficult to solve because of their complexity and size. In particular, forward–backward stochastic differential equations (FBSDEs) are a new technique that is showing ways to solve problems for which there is yet to be a solution. This project's focus will be on problems that cannot use existing software because the decision-making processes require intensive consideration of all possible outcomes in the modelled environment. In comparison to previous optimisation methods, the FBSDE approach is easier to work with and much more informative. The project's main potential applications are multiplayer games with mean-field interaction and financial markets with partial information.Read moreRead less
Advanced Monte Carlo Methods for Spatial Processes. The modeling and analysis of spatial data relies more and more on sophisticated Monte Carlo simulation methods. However, with the growing complexity of today's spatial data, traditional Monte Carlo methods increasingly face difficulties in terms of speed and accuracy. The aim of this project is to develop new theory and applications at the interface of Monte Carlo methods and spatial statistics, building upon exciting theoretical and computatio ....Advanced Monte Carlo Methods for Spatial Processes. The modeling and analysis of spatial data relies more and more on sophisticated Monte Carlo simulation methods. However, with the growing complexity of today's spatial data, traditional Monte Carlo methods increasingly face difficulties in terms of speed and accuracy. The aim of this project is to develop new theory and applications at the interface of Monte Carlo methods and spatial statistics, building upon exciting theoretical and computational advances in both areas in recent years. The research will stimulate the design of microscopic and macroscopic complex spatial structures with superior properties, such as composite materials, solar cells, telecommunication networks, mining operations, and road systems.Read moreRead less
Random walks with long memory. This project aims to study novel random walk models with long memory, including systems of multiple random walkers that interact through their environment. This would provide a mathematical understanding of phenomena such as aggregation in colonies of bacteria, and ant colony optimisation algorithms. The project aims to produce highly cited publications, and to train future researchers.
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