Discovery Early Career Researcher Award - Grant ID: DE140100993
Funder
Australian Research Council
Funding Amount
$293,520.00
Summary
Mathematics of importance: The optimal importance sampling algorithm for estimating the probability of a black swan event. Rare event simulation and modelling is critical to our understanding of high-cost hard-to-predict events such as nuclear accidents, natural disasters, and financial crises. Quantitative analysis of such high-impact events demands the accurate estimation of the probability of occurrence of such rare events. In realistic models this probability is very difficult to estimate, ....Mathematics of importance: The optimal importance sampling algorithm for estimating the probability of a black swan event. Rare event simulation and modelling is critical to our understanding of high-cost hard-to-predict events such as nuclear accidents, natural disasters, and financial crises. Quantitative analysis of such high-impact events demands the accurate estimation of the probability of occurrence of such rare events. In realistic models this probability is very difficult to estimate, because exact simple analytical formulas are not available and the existing estimation methods fail spectacularly. There is an urgent need for new efficient methodology. This project develops a new Monte Carlo method that will be able to estimate reliably and accurately rare-event probabilities. Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE160101147
Funder
Australian Research Council
Funding Amount
$294,336.00
Summary
Predicting extremes when events occur in bursts. This project seeks to advance knowledge in extreme value theory. Extreme value theory is essential to quantify risks in complex systems, such as the risk of network failures. Current statistical models for the occurrence of extremes assume that events happen regularly. This assumption, however, is at odds with human actions and many biological and physical events, which occur in bursts. There is a strong need to understand the effect of such ‘burs ....Predicting extremes when events occur in bursts. This project seeks to advance knowledge in extreme value theory. Extreme value theory is essential to quantify risks in complex systems, such as the risk of network failures. Current statistical models for the occurrence of extremes assume that events happen regularly. This assumption, however, is at odds with human actions and many biological and physical events, which occur in bursts. There is a strong need to understand the effect of such ‘bursty dynamics’ on the frequency and magnitude of extreme events. This project aims to develop extreme value theory for bursty events and thus lay the mathematical groundwork for the estimation and prediction of extremes in a variety of scientific contexts.Read moreRead less
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
Discovery Early Career Researcher Award - Grant ID: DE130100819
Funder
Australian Research Council
Funding Amount
$281,600.00
Summary
Measuring the improbable: optimal Monte Carlo methods for rare event simulation of maxima of dependent random variables. Some events occurring with low frequency can have dramatic consequences: natural catastrophes, economic crises, system malfunctions. Estimating their probabilities is a very difficult problem. This project will develop new simulation methods capable of delivering the most precise and efficient estimators for the probabilities of such events.
Discovery Early Career Researcher Award - Grant ID: DE130100291
Funder
Australian Research Council
Funding Amount
$374,595.00
Summary
Adaptive control of stochastic queueing networks. Queues of items competing for service appear on the road, in health-care, in manufacturing and in communication systems. This project will set up methodology for adaptive control and resource allocation for stochastic queueing network models applicable to a variety of scenarios accounting for parameter uncertainty.
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.
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
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
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.