Random network models with applications in biology. Complex biological systems consist of a large number of interacting agents or components, and so can be studied using mathematical random network models. We aim to gain deeper insights into the laws emerging as the random networks evolve in time. This can help us to deal with dangerous disease epidemics and better understand the human brain.
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
Asymptotic Expansions and Large Deviations in Probability and Statistics: Theory and Applications. Statistics is the major enabling science in a number of disciplines. This is fundamental research in probability and statistics but it has wide applications in Biology and Social Sciences which will ultimately be of national benefit. The behaviour of self normalized sums is an exciting new area of fundamental research that has implications for the application of statistics in many areas. U-statist ....Asymptotic Expansions and Large Deviations in Probability and Statistics: Theory and Applications. Statistics is the major enabling science in a number of disciplines. This is fundamental research in probability and statistics but it has wide applications in Biology and Social Sciences which will ultimately be of national benefit. The behaviour of self normalized sums is an exciting new area of fundamental research that has implications for the application of statistics in many areas. U-statistics for dependent situations has direct application to understanding financial time series and the analysis of sample survey data. Saddlepoint methods provide extremely accurate approximations in a number of important applications.
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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
Discovery Early Career Researcher Award - Grant ID: DE200100896
Funder
Australian Research Council
Funding Amount
$427,008.00
Summary
How to beat model uncertainty with more information. Experience of the 2008 financial crisis exposed a weakness in our over-reliance on mathematical models. The main aim of this project is to develop mathematical tools to investigate the role of information in reducing model uncertainty. The project will undertake pressing research in robust finance, which is now one of the most active and dynamic topics in financial mathematics. It expects to quantify the value of information under uncertainty ....How to beat model uncertainty with more information. Experience of the 2008 financial crisis exposed a weakness in our over-reliance on mathematical models. The main aim of this project is to develop mathematical tools to investigate the role of information in reducing model uncertainty. The project will undertake pressing research in robust finance, which is now one of the most active and dynamic topics in financial mathematics. It expects to quantify the value of information under uncertainty in mathematical modelling. It will generate new knowledge in probability theory and stochastic processes providing a significant mathematical contribution in its own right.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
Empirical saddlepoint approximations and self-normalized limit theorems. Finite population sampling and resampling methods such as the bootstrap and randomization methods are central in a number of areas of application and M-estimates are the major method used to give robust methods under mild conditions; in both these areas statistics are used which are Studentized or self-normalized. We will develop asymptotic approaches for such statistics. Saddlepoint and empirical saddlepoint methods will ....Empirical saddlepoint approximations and self-normalized limit theorems. Finite population sampling and resampling methods such as the bootstrap and randomization methods are central in a number of areas of application and M-estimates are the major method used to give robust methods under mild conditions; in both these areas statistics are used which are Studentized or self-normalized. We will develop asymptotic approaches for such statistics. Saddlepoint and empirical saddlepoint methods will be used to give methods which have second order relative accuracy in large deviation regions and we will obtain limit results and Edgeworth approximations. Emphasis will be on obtaining results under weak conditions necessary for applications.Read moreRead less
Asymptotics in non-linear cointegrating regression: theory and applications. This project provides fundamental research in statistics, econometrics and probability. The results on martingales and nonlinear functionals of integrated stochastic processes will apply to a range of statistical, empirical finance and economic models.
Non-linear cointegrating regression with endogeneity. This project aims to develop the asymptotic theory of estimation and statistical inference in models concerned with non-linear co-integrating regression with endogeneity and long memory. This project will tackle a number of long-standing technical problems related to non-linear covariance functionals and non-linear transformation of nonstationary time series. This project is intended to provide technical tools for practitioners to study the l ....Non-linear cointegrating regression with endogeneity. This project aims to develop the asymptotic theory of estimation and statistical inference in models concerned with non-linear co-integrating regression with endogeneity and long memory. This project will tackle a number of long-standing technical problems related to non-linear covariance functionals and non-linear transformation of nonstationary time series. This project is intended to provide technical tools for practitioners to study the long-run relationship of economic variables, and could apply to a range of statistical, empirical finance and economic models, enhancing national leadership in these areas.Read moreRead less