New Directions in Bayesian Statistics: formulation, computation and application to exemplar challenges. Bayesian statistics is a fundamental statistical and machine learning approach for density estimation, data analysis and inference. However, there remain open questions regarding the formulation of the model, the likelihood and priors, and efficient computation. This project proposes new approaches that address these issues, and applies them to two exemplar challenges: the impact of climate ch ....New Directions in Bayesian Statistics: formulation, computation and application to exemplar challenges. Bayesian statistics is a fundamental statistical and machine learning approach for density estimation, data analysis and inference. However, there remain open questions regarding the formulation of the model, the likelihood and priors, and efficient computation. This project proposes new approaches that address these issues, and applies them to two exemplar challenges: the impact of climate change on the Great Barrier Reef and better understanding neurological diseases related aging, in particular Parkinson's Disease. Read moreRead less
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.
Generalised Degrees of Freedom and Probabilistic Regularisation. This project intends to develop novel statistical tools for more accurate prediction by taking account of model complexity and uncertainties associated with the fitting procedure. The project also plans to develop a novel shrinkage approach via new penalty functions to avoid over-fitting and asymptotic properties. The key applications may include genetic studies where the number of predictors is large and biological experiments whe ....Generalised Degrees of Freedom and Probabilistic Regularisation. This project intends to develop novel statistical tools for more accurate prediction by taking account of model complexity and uncertainties associated with the fitting procedure. The project also plans to develop a novel shrinkage approach via new penalty functions to avoid over-fitting and asymptotic properties. The key applications may include genetic studies where the number of predictors is large and biological experiments where multivariate and temporal data are often collected – for example economical breeding in animal and fish farming and more effectively detecting the genes of interest in genetic studies on human, animals and plants.Read moreRead less
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.
Robust inferences for analysis of longitudinal data. This project will develop novel statistical tools. Outcomes of this project will enable more reliable data analysis and more cost effective designs in environmental and biological studies.
Precision ecology: the modern era of designed experiments in plant ecology. This project aims to develop the field of precision ecology, forging a new era of designed experiments where sampling is informed by research questions and what is known about the ecological process being studied. Through the development of novel statistical methods, new experiments globally will be designed to answer important ecological questions including what influence abiotic and biotic factors have on plant commun ....Precision ecology: the modern era of designed experiments in plant ecology. This project aims to develop the field of precision ecology, forging a new era of designed experiments where sampling is informed by research questions and what is known about the ecological process being studied. Through the development of novel statistical methods, new experiments globally will be designed to answer important ecological questions including what influence abiotic and biotic factors have on plant communities over time and different spatial scales. Expected outcomes include new methods and tools that will modernise how future experiments will be conducted in plant ecology. This will provide significant transdisciplinary benefits including new statistical methods that target scientific discovery in ecological studies.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE160100741
Funder
Australian Research Council
Funding Amount
$382,274.00
Summary
Tractable Bayesian algorithms for intractable Bayesian problems. This project seeks to develop computationally efficient and scalable Bayesian algorithms to estimate the parameters of complex models and ensure inferences drawn from the models can be trusted. Bayesian parameter estimation and model validation procedures are currently computationally intractable for many complex models of interest in science and technology. These include biological processes such as the efficacy of heart disease, ....Tractable Bayesian algorithms for intractable Bayesian problems. This project seeks to develop computationally efficient and scalable Bayesian algorithms to estimate the parameters of complex models and ensure inferences drawn from the models can be trusted. Bayesian parameter estimation and model validation procedures are currently computationally intractable for many complex models of interest in science and technology. These include biological processes such as the efficacy of heart disease, wound healing and skin cancer treatments. Potential outcomes of the project include new algorithms to significantly economise computations and improved understanding of the mechanisms of experimental data generation. Improved models of wound healing, skin cancer growth and heart physiology supported by these algorithms could improve population health.Read moreRead less
Random Discrete Structures: Approximations and Applications. The behaviour of many real world systems can be modelled by random discrete structures evolving over time. For example, the sizes of populations of frogs in some close patches of forests can be modelled as interacting random processes. The aim of the project is to investigate large discrete random structures that arise from real world application in areas such as biology, complex networks and insurance. The proposed project is at the i ....Random Discrete Structures: Approximations and Applications. The behaviour of many real world systems can be modelled by random discrete structures evolving over time. For example, the sizes of populations of frogs in some close patches of forests can be modelled as interacting random processes. The aim of the project is to investigate large discrete random structures that arise from real world application in areas such as biology, complex networks and insurance. The proposed project is at the interface of mathematics and 'big data' applications and so the work of the project aims to provide theoretical and heuristic underpinnings useful in the algorithms and techniques of practitioners. Understanding the applications in the project requires new, broadly applicable methods and developing such is a complementary aim.Read moreRead less
Understanding the effects of individual variation on population dynamics. Recent empirical studies have shown that trait variation among individuals in a population can have a significant impact on population dynamics. Given the considerable resources devoted to managing populations in Australia, it is vital individual variation be understood. This project will use the tools of modern probability theory to investigate the effect of trait variation on population-level quantities, such as the prob ....Understanding the effects of individual variation on population dynamics. Recent empirical studies have shown that trait variation among individuals in a population can have a significant impact on population dynamics. Given the considerable resources devoted to managing populations in Australia, it is vital individual variation be understood. This project will use the tools of modern probability theory to investigate the effect of trait variation on population-level quantities, such as the probability of extinction and the long term equilibrium level. This work will lead to better strategies for managing invasive diseases and pests, thus helping to protect Australia's biodiversity. The methods developed will be applicable to areas beyond population dynamics.Read moreRead less
A Novel Approach to Semi-Supervised Statistical Machine Learning. Recent successes in the construction of classifiers for making diagnoses and predictions are due in part to their using much data labelled with respect to their class of origin. But typically there are little labelled data but plentiful unlabelled data. The goal of semi-supervised learning (SSL) is to leverage large amounts of unlabelled data to improve the performance using only small labelled datasets and so SSL is of paramount ....A Novel Approach to Semi-Supervised Statistical Machine Learning. Recent successes in the construction of classifiers for making diagnoses and predictions are due in part to their using much data labelled with respect to their class of origin. But typically there are little labelled data but plentiful unlabelled data. The goal of semi-supervised learning (SSL) is to leverage large amounts of unlabelled data to improve the performance using only small labelled datasets and so SSL is of paramount importance to applications where it is expensive or impractical to obtain much labelled data. The project is to develop a novel SSL approach that adopts a missingness mechanism for the missing labels to build a classifier that not only improves accuracy but it can be greater than if the missing labels were known.
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