Extending Cognitive Models to Account for Individual Differences. Despite their impressive achievements, cognitive models of memory retention, category learning, and stimulus representation usually model people as ?invariants?, concentrating on what makes them the same. This project aims to extend all three types of model to also treat people as ?individuals?, and account for how people are different. Advanced model selection methods will be used to do this in a way that is complete, general, an ....Extending Cognitive Models to Account for Individual Differences. Despite their impressive achievements, cognitive models of memory retention, category learning, and stimulus representation usually model people as ?invariants?, concentrating on what makes them the same. This project aims to extend all three types of model to also treat people as ?individuals?, and account for how people are different. Advanced model selection methods will be used to do this in a way that is complete, general, and principled. The outcome will be a set of new theoretical models, and new algorithms to learn the models from empirical data, that explain the differences between people in remembering, learning and representing information.Read moreRead less
Theory and applications of Bayesian and likelihood analyses for finite mixture, random effect and multinomial models. The expected outcomes of the project are: to establish the scientific
value of modern Bayesian methods for statistical inference in a wider
range of applications than previously available, to contribute to the greater unification of the current theories of statistical inference which are to some extent in conflict, and to provide a set of Bayesian analytic tools implemented in ....Theory and applications of Bayesian and likelihood analyses for finite mixture, random effect and multinomial models. The expected outcomes of the project are: to establish the scientific
value of modern Bayesian methods for statistical inference in a wider
range of applications than previously available, to contribute to the greater unification of the current theories of statistical inference which are to some extent in conflict, and to provide a set of Bayesian analytic tools implemented in widely available, free and open-source statistical software.
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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
Rare Event Simulation with Heavy Tails. The project provides a rigorous way to enhance our understanding of the mechanisms that bring about catastrophic rare events such as urban flooding, electricity shortages and financial bankrupcy. Australia is at the forefront of exciting recent developments in rare event simulation. The advancement of the knowledge in this area will generate a competitive advantage for various sections of the Australian industry, including the areas of industrial reliabili ....Rare Event Simulation with Heavy Tails. The project provides a rigorous way to enhance our understanding of the mechanisms that bring about catastrophic rare events such as urban flooding, electricity shortages and financial bankrupcy. Australia is at the forefront of exciting recent developments in rare event simulation. The advancement of the knowledge in this area will generate a competitive advantage for various sections of the Australian industry, including the areas of industrial reliability, finance and insurance, were accurate simulation techniques are becoming increasingly important.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
Stein's method for probability approximation. Data of counts in time, such as incoming calls in telecommunications and the clusters of palindromes in a family of herpes-virus genomes, arise in an extraordinarily diverse range of fields from science to business. These problems can be modelled by sums of random variables taking values 0 and 1 in probability theory, thus permitting approximate calculations which are often good enough in practice. This project will obtain such approximate solutions ....Stein's method for probability approximation. Data of counts in time, such as incoming calls in telecommunications and the clusters of palindromes in a family of herpes-virus genomes, arise in an extraordinarily diverse range of fields from science to business. These problems can be modelled by sums of random variables taking values 0 and 1 in probability theory, thus permitting approximate calculations which are often good enough in practice. This project will obtain such approximate solutions and estimate the errors involved. Applications include analysis of data in insurance, finance, flood prediction in hydrology.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