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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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.
Markov Field Theory applied to Sensor Networks Analysis and Design. Ad hoc and sensor networks have a wide range of applications in defence, emergency services and agriculture because they do not require telecommunications infrastructure such as base stations or access points, hence are relatively easy to deploy in harsh environments. This project aims at improving the theoretical understanding of sensor and ad hoc networks, which enable improvements in performance in such networks. Australian d ....Markov Field Theory applied to Sensor Networks Analysis and Design. Ad hoc and sensor networks have a wide range of applications in defence, emergency services and agriculture because they do not require telecommunications infrastructure such as base stations or access points, hence are relatively easy to deploy in harsh environments. This project aims at improving the theoretical understanding of sensor and ad hoc networks, which enable improvements in performance in such networks. Australian defence industry and emergency services will benefit from this research by gaining access to improved ad hoc communications networks. The agricultural sector will also benefit from the improved sensor networks in applications such as monitoring soil conditions, stock and crop levels. 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