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
Meta-research: Using Research To Increase The Value Of Health And Medical Research
Funder
National Health and Medical Research Council
Funding Amount
$631,370.00
Summary
Improving the return on investment in health and medical research will produce more and faster discoveries that enhance the lives of all Australians. Many problems in the research process are well known and have been pervasive for decades. I will use the research process to improve the research process. I will improve Australia's health and medical research workforce and the quality of the research they produce, creating benefits in multiple fields that last long into the future.
Complex data, model selection and bootstrap inference. The project will provide new statistical methods and associated software for the analysis and modelling of complex data, as well as quality research training. This project will benefit researchers in statistics and users of statistics who encounter the complex data considered in this project and who need to model and make inferences from these data. Since these kinds of data arise in many areas (such as medicine, genetics, chemistry etc), ....Complex data, model selection and bootstrap inference. The project will provide new statistical methods and associated software for the analysis and modelling of complex data, as well as quality research training. This project will benefit researchers in statistics and users of statistics who encounter the complex data considered in this project and who need to model and make inferences from these data. Since these kinds of data arise in many areas (such as medicine, genetics, chemistry etc), Australia and Australian industry will ultimately benefit from the proposed research. The strengthening of international link and the training of highly trained research scientists in an area of national importance will also benefit Australia.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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Modelling mean and dispersion using fixed and random effects. The aims of the project are to develop methods for joint mean and dispersion modelling using fixed and random effects, in the generalized linear models context and for Gaussian longitudinal data. The significance is the more efficient, precise and appropriate analysis of data arising from many areas of application. The expected outcomes are therefore better methods of analysis, software to carry the analyses out, and potentially impor ....Modelling mean and dispersion using fixed and random effects. The aims of the project are to develop methods for joint mean and dispersion modelling using fixed and random effects, in the generalized linear models context and for Gaussian longitudinal data. The significance is the more efficient, precise and appropriate analysis of data arising from many areas of application. The expected outcomes are therefore better methods of analysis, software to carry the analyses out, and potentially important results in applications.Read moreRead less
Bootstrap methods for data with multiple errors. This project will provide new methods for data analysis and quality research training. The results will benefit researchers in statistics and users of statistics who encounter data with multiple errors and who need to make inferences from these data. The many areas from which such data arise (including medicine, genetics, chemistry, education, social surveys etc) mean that Australia and Australian Industry will also ultimately benefit from the r ....Bootstrap methods for data with multiple errors. This project will provide new methods for data analysis and quality research training. The results will benefit researchers in statistics and users of statistics who encounter data with multiple errors and who need to make inferences from these data. The many areas from which such data arise (including medicine, genetics, chemistry, education, social surveys etc) mean that Australia and Australian Industry will also ultimately benefit from the research. The strengthening of international links and the training of highly trained researchers will also benefit the Australian community.Read moreRead less
International Networks in Applied Bayesian Statistics: improving Australia''s knowledge through intelligent data analysis and modelling. National benefits of this project are fourfold: (i) new international networks between Australia, Southern Africa, France and USA in the priority area of mathematical sciences; (ii) state-of-the-art Bayesian statistical methods for integrating and analyzing non-standard data and diverse information sources, including expert opinion, in order to solve complex pr ....International Networks in Applied Bayesian Statistics: improving Australia''s knowledge through intelligent data analysis and modelling. National benefits of this project are fourfold: (i) new international networks between Australia, Southern Africa, France and USA in the priority area of mathematical sciences; (ii) state-of-the-art Bayesian statistical methods for integrating and analyzing non-standard data and diverse information sources, including expert opinion, in order to solve complex problems in environment, industry, health, defence; (iii) direct contribution to solution of global environmental problems, specifically water quality, threatened species and environmental risk; (iv) superior training of the next generation of the global community of researchers in applied statistics.Read moreRead less
New methods for small group analysis from sample surveys. National and state averages of statistics on issues such as unemployment, salinity, drought impact, and health often hide large differences between population sub-groups and between small areas. This local variation needs to be understood so that effective policies can be developed and carried out efficiently and their impact monitored. This project will provide, for the first time, robust and efficient methods for providing information o ....New methods for small group analysis from sample surveys. National and state averages of statistics on issues such as unemployment, salinity, drought impact, and health often hide large differences between population sub-groups and between small areas. This local variation needs to be understood so that effective policies can be developed and carried out efficiently and their impact monitored. This project will provide, for the first time, robust and efficient methods for providing information on these variations using data from large-scale national and state surveys. This will lead to significant improvements in the data available for small population groups and small areas, allowing better targeting of policies aimed at addressing local differences.Read moreRead less