Statistical Inference for Probability-Linked Longitudinal Data. The Strategic Roadmap for the Australian Government's National Collaborative Research Infrastructure Strategy states that analysis of linked data, and particularly linked longitudinal data, has the potential to revolutionise Australian public health research. Similar benefits should flow from analysis of linked datasets in other areas, e.g. the Statistical Longitudinal Census Dataset that the Australian Bureau of Statistics intends ....Statistical Inference for Probability-Linked Longitudinal Data. The Strategic Roadmap for the Australian Government's National Collaborative Research Infrastructure Strategy states that analysis of linked data, and particularly linked longitudinal data, has the potential to revolutionise Australian public health research. Similar benefits should flow from analysis of linked datasets in other areas, e.g. the Statistical Longitudinal Census Dataset that the Australian Bureau of Statistics intends to create by linking individual records across censuses. These benefits will be maximised by controlling the impact of linkage error when analysing these datasets. This proposal will develop the statistical theory and related methodology to solve this problem in a statistically efficient manner.Read moreRead less
New methods for modelling real-world extremes. This project aims to develop new theory and methods for analysing and predicting extreme values observed in real-world processes. Many existing techniques are limited by convenient mathematical assumptions that commonly do not hold in practice: dependence at asymptotic levels, process stationarity, and that the observed data are direct measurements of the process of interest. As a result, using these techniques may produce undesirable results. Expec ....New methods for modelling real-world extremes. This project aims to develop new theory and methods for analysing and predicting extreme values observed in real-world processes. Many existing techniques are limited by convenient mathematical assumptions that commonly do not hold in practice: dependence at asymptotic levels, process stationarity, and that the observed data are direct measurements of the process of interest. As a result, using these techniques may produce undesirable results. Expected outcomes of this project include theoretically justified data analysis techniques that can accurately model extreme values seen in the real world. Project benefits include more realistic analyses of nationally important applications in climate, bushfire insurance risk, and anomaly detection.Read moreRead less
A likelihood-based approach to combined surveys inference. This project focuses on the development of statistical theory for efficient integration of information across multiple complex sample surveys. It will develop theory and methodology that will answer complex questions about relationships between important social, economic and health related variables that are presently measured in separate surveys.
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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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
Fundamental Studies in System Identification. To operate a dynamic system such as a chemical process plant or an economy one needs two things; the equations describing the system; a way of regulating the system to provide desired outcomes. System identification provides the first; control engineering design provides the second. This proposal addresses three important problems in system identification and control. Firstly since the equations can never be known precisely we aim to determine what i ....Fundamental Studies in System Identification. To operate a dynamic system such as a chemical process plant or an economy one needs two things; the equations describing the system; a way of regulating the system to provide desired outcomes. System identification provides the first; control engineering design provides the second. This proposal addresses three important problems in system identification and control. Firstly since the equations can never be known precisely we aim to determine what is the best one can do? Secondly to provide then tight error bounds for the control design;
thirdly to develop new methods for some hitherto unresolved problems in system identification.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
Efficient Design for Generalized Linear Models. In industrial, commercial and social research, we collect data in order to predict the outcome of a process based on the inputs to that process. We want to maximize the information that is gained from the data. Good planning is crucially important to achieve this. This project will determine how best to select the inputs to the process for many situations that occur in research. A computer package to answer these questions will be written. The nati ....Efficient Design for Generalized Linear Models. In industrial, commercial and social research, we collect data in order to predict the outcome of a process based on the inputs to that process. We want to maximize the information that is gained from the data. Good planning is crucially important to achieve this. This project will determine how best to select the inputs to the process for many situations that occur in research. A computer package to answer these questions will be written. The nation will benefit from a fundamental increase in efficiency of research and, therefore, in efficient use of research dollars.Read moreRead less
Innovations in Bayesian likelihood-free inference. Bayesian inference is a statistical method of choice in applied science. This project will develop innovative tools which permit Bayesian inference in problems considered intractable only a few years ago. These methods will expedite advances in multidisciplinary research across a range of applications. With these foundations, this project will accelerate national research efforts into improving frameworks for projecting trends in water availabil ....Innovations in Bayesian likelihood-free inference. Bayesian inference is a statistical method of choice in applied science. This project will develop innovative tools which permit Bayesian inference in problems considered intractable only a few years ago. These methods will expedite advances in multidisciplinary research across a range of applications. With these foundations, this project will accelerate national research efforts into improving frameworks for projecting trends in water availability and management, the impact of climate extremes, telecommunications engineering, HIV and infectious disease modelling and biostatistics. With many sectors unable to recruit appropriately trained statisticians within Australia, this project will train four PhD students in Bayesian statistics.
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