Current Funded Research Projects in Bristol Statistics

The Statistics Group has won major strategic funding in the form of a Science and Innovation Award from the EPSRC. The multi-million pound grant - one of the largest ever awarded to a mathematics department - will fund a new initiative entitled SuSTaIn (Statistics underpinning Science, Technology and Industry), to be led by Peter Green FRS, Guy Nason and Christophe Andrieu. It will support an ambitious programme to conduct and disseminate internationally-leading research in mathematical statistics, equipping the discipline to face the challenges of future applications. In partnership with the University of Bristol, the Award will fund a new Chair of Statistics, several Lectureships, Postdocs and Studentships, and activities including workshops and research kitchens, visitor support, an international conference and a comprehensive programme of research training for graduate students.

A project to utilize multiscale lifting transforms for the estimation, modelling and forecasting of stochastic volatility on networks both across networks and in time. Part of a larger multidisciplinary initiative involving Computer Science, Experimental Psychology, Engineering Mathematics and Electrical and Electronic Engineering and Statistics. Staff involved (in Statistics): Guy Nason.

The aims of the project are to contribute to the theory of self-interacting and perturbed Markov chain processes and to develop their application to the area of Markov chain Monte Carlo methods applied to statistical inference.With regard to the development of computational methods for statistical inference, we aim at developing novel self-tuning, approximate and/or exact, efficient inference techniques for large scale systems, with an emphasis on latent variable models. With regard to the theory of self-exciting and perturbed Markov chains, we aim to complete the theoretical understanding of the ergodicity of self-tuning MC algorithms, to analyse recently proposed approximate MC algorithms (e.g. Monte Carlo within Metropolis), and more generally extend the theory of stochastic approximation with Markovian dynamic, and develop a more general theory of reinforced, or self-interacting, processes with Markovian dynamic (e.g. reinforced random walk). (with associated grant "A high quality toolbox of computational methods for statistical inference."). Staff involved: Christophe Andrieu

This project is designed to develop and create novel statistical methods based on the multiscale lifting transform. Lifting can be thought of as a generalization of the wavelet transform. Lifting enables the decomposition of various types of object (signal/image) into a multiscale form that can be easier to manipulate for a number of interesting purposes. Lifting is especially attractive for statistical problems as it enables the analysis of irregularly distributed data that is often found in spatial data contexts but is general enough to also be able to tackle problems specified on networks. So, for example, it is possible to model the delays in a network (such as the Internet or transportation networks) in a multiscale network and to follow its time evolution. We also intend to use lifting methods to model and analyse irregularly spaced time series and also to approach various interesting bioinformatics problems in protein modelling using lifting. Staff involved: Guy Nason.

A large multidisciplinary project involving Electrical and Electronic Engineering and Experimental Psychology. Statistics components include "Wavelet methods for data fusion", "Multiscale Network Visualization". Staff involved: Guy Nason, Christophe Andrieu, Peter Green, Alessandro Cardinali.

This fellowship has been awared to Oliver Zobay, with the following objectives: (a) to develop new methodology for computational Bayesian inference on the basis of variational techniques and their combination with other methods. To reach this aim, it is planned, e.g., to test and apply variational techniques used in other areas of science, to combine variational and Monte Carlo methods, or to optimise and extend existing approaches. A particular focus will be put on areas in which the established techniques for Bayesian inference perform badly. (b) to develop software implementations of the new methods and make them publicly available so that they can easily be used by practitioners of Bayesian inference. (c) to obtain an overview of the existing variational methods used in Bayesian inference and related fields, their strength, weaknesses, areas of applicability, etc. On the basis of this overview, the fields where the development of new methodology is necessary and feasible will be defined which is an important prerequisite for the main research objectives. Staff involved: Oliver Zobay and Peter Green.

This project deals with novel applications of sequential Monte Carlo methods (also known as particle filters, or Monte Carlo filters). SMC methods are already used successfully in many dynamic applications, particularly in engineering (target tracking, signal processing etc.). Our aim is to prove that sequential Monte Carlo methodology can also be very effective in completely different scenarios, especially in "complex", non-sequential Bayesian problems. By "complex", we mean "not dealt with satisfactorily by standard methods (e.g. MCMC)"; this may be due to the large dimension of the problem (in terms of the sample, the parameter, or both), the irregularity of the posterior density (e.g. mixtures), the intractability of the model, etc. Staff involved: Nicolas Chopin.

A joint project with Prof Guy Rutter, Biochemistry, Bristol to both investigate new multiscale approaches in bioinformatics and vesicle object tracking. Staff involved: Guy Nason.

The project aims to develop novel statistical tools to find biologically meaningful groupings in gene expression profiles across multiple samples. It will use Bayesian hierarchical models to integrate sources of variability, prior knowledge, assessment of uncertainty and the flexibility to cope with variable dimension problems. To ensure efficient knowledge transfer to the Microarray community, the tools developed will be installed in the Microarray Centre at Imperial College. The project is built around a close collaboration between statisticians and molecular biologists. Through these interactions, the essential interplay between relevant scientific questions arising from genomics experiments and model development will be accomplished. Staff involved: Peter Green (with collaborators in Biostatistics, Imperial College).

Project to investigate and develop the role of wavelets within statistics and probability. Main areas of interest are wavelet shrinkage, confidence intervals, locally stationary time series analyses, multiscale variable transformations, links with experimental design, lifting for irregular data. Staff involved: Guy Nason.

The goal of this project is to investigate division of labour and information flow in social insect colonies, seeking to understand the role that environmental variability, group size and spatial structure play in the evolution of different task allocation mechanisms. Results will shed light on how social insects perform complex collective behaviours even though they individually have limited cognitive abilities and access to only local information. Understanding these processes has wide implications for the study of other complex systems. Staff involved: John McNamara, Sean Collins, and Professors Nigel Franks and Alasdair Houston from Biological Sciences.

The aim of the project is twofold: (a) first to pursue the work on the methodological and theoretical aspects of adaptive Monte Carlo techniques initiated during an earlier collaboration. These adaptive techniques aim at facilitating the use of the popular Monte Carlo techniques by automatising their tuning (b) to develop the connection between the tools developed to analyse adaptive Monte Carlo techniques to the field of reinforced process, with an emphasis on reinforced random walks for example. Staff involved: Christophe Andrieu (with CREST-ENSAE, Paris).

How does a pair of animals or humans come to an agreement? Most current game-theoretic models assume that each individual makes its own decision independently of that of its partner. This assumption is unrealistic in most social interactions. This project combines mathematical modelling with experimental tests on the Kentish plover to investigate how the animals interact and how they arrive at negotiated solutions. Staff involved: John McNamara, Professors Innes Cuthill and Alasdair Houston from Biological Sciences and Dr Tamas Szekely for Bath University.

Seals exhibit a variety of life history and energetic strategies and are found in a range of environments that vary in their seasonality and predictability. This project seeks insights into how environmental forces shape the life histories of long-lived mammals, using seals as a study group. The predictions of new theoretical models will be compared to data on the life histories and the global distributions of the 33 seal species. The study will generate hypotheses about the relationship between life history evolution, population dynamics and environmental variability in general, but also has straightforward applications to conservation biology. Staff involved: John McNamara, Professor Alasdair Houston from Biological Sciences, and Professor Ian Boyd from the University of St Andrews.

The aim of the project is to investigate approximate and reduced complexity techniques that are well known and developed in the statistical and computer science communities in order to carry out efficient statistical inference in the context of wireless telecommunication, with an emphasis on MIMO (Multiple Input, Multiple Output) scenarios and turbo equalization. Staff involved: Christophe Andrieu

Monte Carlo methods are powerful techniques that are used to analyse complex real-world data, with applications in diverse fields including genetics, computer science, engineering and Bayesian statistics. However they rely on parameters that need to be carefully tuned for each individual application, a task that can prove impossible even for an expert statistician. This research project will develop adaptive Monte Carlo algorithms, that automatically tune themselves by monitoring current performance levels and adjusting parameters accordingly. Optimal parameter values can then be learned for each individual problem, without the need for complex preliminary analyses. Staff involved: David Leslie.

Part of a large collaborative project aiming to develop techniques, methods and architectures for modelling, designing and building decentralised systems that can bring together information from a variety of heterogeneous sources in order to take informed actions. The techniques of game theoretical learning will be applied to design agents that are incentivised to behave in particular ways. More precisely, the agents should be designed so that a collection of agents learning together should move towards particular equilibrium points, and exhibit stability, fairness and efficiency. In addition, these goals must be achieved in situations of limited information with significant communication constraints. Staff involved: David Leslie.

Accurate modelling and forecasting of financial time series volatility is of interest to both practitioners and theoretical statisticians. Typically, volatility is modelled as a stationary nonlinear stochastic process, such as ARCH or any of its numerous extensions. In this project, we investigate various theoretical and practical aspects of the recently proposed locally stationary ARCH model, whose parameters evolve over time in a "slow" fashion. Staff involved: Piotr Fryzlewicz.

Random processes have been enormously widely used to model phenomena in different sciences, ranging from physics to biology and from economics to sociology. However, only recently have history-dependent stochastic processes started receiving attention. Among them a special role is played by "nostalgic" reinforced processes, which are more likely to visit the states they have already visited. This grant provides a financial support for a visit to the University of British Columbia to establish collaboration with Professor Vlada Limic in the area of reinforced processes and their applications, as well as other probabilitists there. Staff involved: Stas Volkov.

A computer model is contructed to model the flow of water through the floodplain and predicts flood extent. Unfortunately this computer model will require some inputs that we have no means of measuring - we call these the unknown parameters of the model. To use the model for prediction we first need to estimate the values of these unknown parameters by running the model for an observed event and comparing the model output and the observed data (to be improved by Simon). Staff involved: Peter Green.

e-Science is about global collaboration, via the Internet, in key areas of research. At the moment it is difficult to use the Internet as a conferencing tool, and even harder to use it for large-scale computations, but the technical improvements to be developed at the University should allow scientists in Bristol to share data on a global basis, and communicate with colleagues across the world as easily as those in the next room. Staff involved: Guy Nason, Peter Green, and 14 other investigators.

Projects that have recently finished

Standard theory and solution algorithms for Markov Decision Processes (MDPs) or Markov games address finite state and action models for which the system parameters are fully specified. The current focus of this project is to extend the theory and computational algorithms for MDPs to continuous state models, using recently developed function approximation methods for reinforcement learning. The long term aim is to identify the implications for game theoretic models in the context of guidance and control problems. Staff involved: Sean Collins.

The aim of the project is to develop new semi-parametric methods, which can be used for the construction of effective and fair insurance tariffs, a collaboration with Dr. Andreas Christmann at University of Dortmund. Staff involved: Arne Kovac.

Some organisms such as pacific salmon reproduce once and die, while others such as humans typically reproduce many times. Life history theory attempts to understand the evolutionary processes that give this species diversity, and hence account for the relationship between the environment and lifestyle. But this theory largely ignores the physiological mechanisms that mediate trade offs. This project will develop a framework that incorporates mechanism into life history theory. Staff involved: John McNamara.