You may contact a Proposer directly about a specific project or contact the Postgraduate Admissions Secretary with general enquiries.

Title Network performance subject to agent-based dynamical processes
Group(s) Industrial and Applied Mathematics, Statistics and Probability
Proposer(s) Dr Keith Hopcraft, Dr Simon Preston
Description

Networks – systems of interconnected elements – form structures through which information or matter is conveyed from one part of an entity to another, and between autonomous units. The form, function and evolution of such systems are affected by interactions between their constituent parts, and perturbations from an external environment. The challenge in all application areas is to model effectively these interactions which occur on different spatial- and time-scales, and to discover how

i)     the micro-dynamics of the components influence the evolutionary structure of the network, and

ii)    the network is affected by the external environment(s) in which it is embedded.

Activity in non-evolving networks is well characterized as having diffusive properties if the network is isolated from the outside world, or ballistic qualities if influenced by the external environment. However, the robustness of these characteristics in evolving networks is not as well understood. The projects will investigate the circumstances in which memory can affect the structural evolution of a network and its consequent ability to function.

Agents in a network will be assigned an adaptive profile of goal- and cost-related criteria that govern their response to ambitions and stimuli. An agent then has a memory of its past behaviour and can thereby form a strategy for future actions and reactions. This presents an ability to generate ‘lumpiness’ or granularity in a network’s spatial structure and ‘burstiness’ in its time evolution, and these will affect its ability to react effectively to external shocks to the system. The ability of externally introduced activists to change a network’s structure and function - or agonists to test its resilience to attack - will be investigated using the models. The project will use data of real agent’s behaviour.

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Title Fluctuation Driven Network Evolution
Group(s) Industrial and Applied Mathematics, Statistics and Probability
Proposer(s) Dr Keith Hopcraft, Dr Simon Preston
Description

A network’s growth and reorganisation affects its functioning and is contingent upon the relative time-scales of the dynamics that occur on it. Dynamical time-scales that are short compared with those characterizing the network’s evolution enable collectives to form since each element remains connected with others in spite of external or internally generated ‘shocks’ or fluctuations. This can lead to manifestations such as synchronicity or epidemics. When the network topology and dynamics evolve on similar time-scales, a ‘plastic’ state can emerge where form and function become entwined. The interplay between fluctuation, form and function will be investigated with an aim to disentangle the effects of structural change from other dynamics and identify robust characteristics.

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Title Optimising experiments for developing ion channel models
Group(s) Mathematical Medicine and Biology, Statistics and Probability
Proposer(s) Dr Gary Mirams, Dr Simon Preston
Description

Background: in biological systems ion channel proteins sit in cell membranes and selectively allow the passage of particular types of ions, creating currents. Ion currents are important for many biological processes, for instance: regulating ionic concentrations within cells; passing signals (such as nerve impulses); or coordinating contraction of muscle (skeletal muscle and also the heart, diaphragm, gut, uterus etc.). Mathematical ion channel electrophysiology models have been used for thousands of studies since their development by Hodgkin & Huxley in 1952 [1], and are the basis for whole research fields, such as cardiac modelling and brain modelling [2]. It has been suggested that there are problems in identifying which set of equations is most appropriate as an ion channel model. Often it appears different structures and/or parameter values could fit the training data equally well, but they may make different predictions in new situations [3].

Aim: we have been developing novel experimental designs to provide more information about ion channel behaviour from shorter experiments. We would like to improve our techniques – to describe the ion current and also to characterise drug binding to ion channels (which can physically block them and reduce the current that flows to zero, sometimes leading to fatal heart rhythm changes). It is difficult to measure the rate at which drug/ion channel binding occurs and whether it occurs when the channels are open, closed, or both. These factors may be crucial in determining whether novel pharmaceutical compounds are likely to have side effects or not, and there is a need to develop efficient ways to measure them.

Approach: this project will involve computational biophysical modelling (efficient numerical solution of nonlinear ODE systems); the application of statistical techniques to quantify our uncertainty in model parameters and model equations/structure; and some wet-lab laboratory electrophysiology experiments. We will design more information-rich experiments to reduce our uncertainty in the models we develop [4] and work closely with labs to test out experiments we design and improve them.

Eligibility/Entry Requirements: this PhD will suit a graduate with a 1st class degree in Mathematics (or other highly mathematical field such as Physics), ideally at the MMath/MSc level, or an equivalent overseas degree. Prior knowledge of biology is not essential.

Relevant Publications
  • A. L. Hodgkin and A. F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,” J. Physiol., vol. 117, pp. 500–544, 1952.
  • D. Noble, A. Garny, and P. J. Noble, “How the Hodgkin – Huxley equations inspired the Cardiac Physiome Project,” vol. 11, pp. 2613–2628, 2012.
  • M. Fink and D. Noble, “Markov models for ion channels : versatility versus identifiability and speed,” Philos. Trans. A., vol. 367, no. 1896, pp. 2161–79, Jun. 2009.
  • G. R. Mirams, P. Pathmanathan, R. A. Gray, P. Challenor, and R. H. Clayton, “White paper: Uncertainty and variability in computational and mathematical models of cardiac physiology.,” J. Physiol., Mar. 2016.
Other information

Please see Gary Mirams' research homepage for more information.

Title Numerical methods for stochastic partial differential equations
Group(s) Scientific Computation, Statistics and Probability
Proposer(s) Prof Michael Tretyakov
Description

Numerics for stochastic partial differential equations (SPDEs) is one of the central topics in modern numerical analysis. It is motivated both by applications and theoretical study. SPDEs essentially originated from the filtering theory and now they are also widely used in modelling spatially distributed systems from physics, chemistry, biology and finance acting in the presence of fluctuations. The primary objectives of this project include construction, analysis and testing of new numerical methods for SPDEs.

 

Relevant Publications
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Web-page http://www.maths.nott.ac.uk/personal/pmzmt

Title Property Prediction of Composite Components Prior to Production
Group(s) Scientific Computation, Statistics and Probability
Proposer(s) Prof Michael Tretyakov, Prof Frank Ball
Description

Property Prediction of Composite Components Prior to Production

Supervisors: Dr Frank Gommer1*, Prof Michael Tretyakov2*, Prof Frank Ball2 , Dr Louise P. Brown1

University of Nottingham, University Park, Nottingham NG7 2RD, UK

1 Polymer Composites Group, Faculty of Engineering

2 School of Mathematical Sciences

* Contact: F.Gommer@nottingham.ac.uk or Michael.Tretyakov@nottingham.ac.uk

 

This is an exciting opportunity for a postgraduate student to join a vibrant inter-disciplinary team and to work in the modern area of Uncertainty Quantification.

Fibre reinforced composites are increasingly used in the transport industry to decrease the structural weight of a vehicle and thus increase its fuel efficiency. The importance of the UK composite sector is reflected in the current growth rate of 17% pa for high performance composite components and the expected gross value of £2 billion in 2015 [1]. However, due to the large number of production steps and the necessary saturation of the fibre preform with a resin matrix, a significant amount of waste is produced, which may range between 2% and 20% of the production volume [2]. A major cause of rejecting parts is variability in the reinforcement, such as varying yarn spacing and yarn path waviness, which can significantly influence subsequent properties. For example, these variabilities can affect resin flow and may cause dry spots or reduce mechanical properties. This PhD project will enable the successful candidate to work at the forefront of material science, combining engineering standards, applied mathematics and statistics, with a potential of making an impact on the way of manufacturing composite parts in the future.

This proposed doctoral study aims to demonstrate that properties of light-weight fibre reinforced plastics can be predicted in real time before a part is actually manufactured. Data gained from images taken of each layer of a composite during the stacking process are used to determine local geometries and variabilities, within and in-between individual layers [3]. For example, based on the measured textile geometries it will be possible to predict the resin flow within a preform during a liquid composite moulding (LCM) process considering individual variabilities before injection. These specific flow predictions will allow adjustments of the process parameters during the impregnation process to ensure full saturation of the entire preform with a liquid resin matrix. This will be especially useful when a number of inlet and outlet ports are present such as in the case of complex or large parts. The formation of dry spots will be avoided, which will reduce immediate wastage. For these predictions, faster solutions than currently available are necessary. To find such solutions, appropriate advanced statistical techniques and stochastic modelling for quantifying uncertainties in composites production will be developed in the course of the PhD project.

In addition, the developed techniques will also allow virtual testing of a finished component with its specific inherent reinforcement variability. This will make it feasible to customise predictions for every fabricated component. In combination with continuous health monitoring of a structure, it may be possible to estimate the influence of loading conditions, load cycles and damage evaluation. This will also make it possible to predict an individual life expectancy of a part in service. These data can then be used to determine customised inspection intervals for each component.

We require an enthusiastic graduate with a 1st class degree in Mathematics or Engineering, preferably of the MMath/MSc level, with good programming skills and willing to work as a part of an interdisciplinary team. A candidate with a solid background in statistics will have an advantage.

References

[1] CompositesUK. www.compositesuk.co.uk/Information/FAQs/UKMarketValues.aspx.

[2] A. C. Long, Design and Manufacture of Textile Composites: Woodhead Publ, 2005.

[3] F. Gommer, L. P. Brown, and R. Brooks, “Quantification of meso-scale variability and geometrical reconstruction of a textile”, submitted to Compos Part A-Appl S, 2015.

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This project is supported by  EPSRC DTG Centre in Complex Systems and Processes, see elligibility and how to apply at http://www.nottingham.ac.uk/complex-systems/index.aspx

Title Index policies for stochastic optimal control
Group(s) Statistics and Probability
Proposer(s) Dr David Hodge
Description

Since the discovery of Gittins indices in the 1970s for solving multi-armed bandit processes the pursuit of optimal policies for this very wide class of stochastic decision processes has been seen in a new light. Particular interest exists in the study of multi-armed bandits as problems of optimal allocation of resources (e.g. trucks, manpower, money) to be shared between competing projects. Another area of interest would be the theoretical analysis of computational methods (for example, approximative dynamic programming) which are coming to the fore with ever advancing computer power.


Potential project topics could include optimal decision making in the areas of queueing theory, inventory management, machine maintenance and communication networks.

Relevant Publications
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Keywords: multi-armed bandits, dynamic programming, Markov decision processes

Title Semi-Parametric Time Series Modelling Using Latent Branching Trees
Group(s) Statistics and Probability
Proposer(s) Dr Theodore Kypraios
Description

A class of semi-parametric discrete time series models of infinite order where we are be able to specify the marginal distribution of the observations in advance and then build their dependence structure around them can be constructed via an artificial process, termed as Latent Branching Tree (LBT). Such a class of models can be very useful in cases where data are collected over long period and it might be relatively easy to indicate their marginal distribution but much harder to infer about their correlation structure. The project is concerned with the development of such models in continuous-time as well as developing efficient methods for making Bayesian inference for the latent structure as well as the model parameters. Moreover, the application of such models to real data would be also of great interest.

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Title Ion channel modelling
Group(s) Statistics and Probability
Proposer(s) Prof Frank Ball
Description

The 1991 Nobel Prize for Medicine was awarded to Sakmann and Neher for developing a method of recording the current flowing across a single ion channel. Ion channels are protein molecules that span cell membranes. In certain conformations they form pores allowing current to pass across the membrane. They are a fundamental part of the nervous system. Mathematically, a single channel is usually modelled by a continuous time Markov chain. The complete process is unobservable but rather the state space is partitioned into two classes, corresponding to the receptor channel being open or closed, and it is only possible to observe which class of state the process is in. The aim of single channel analysis is to draw inferences about the underlying process from the observed aggregated process. Further complications include (a) the failure to detect brief events and (b) the presence of (possibly interacting) multiple channels. Possible projects include the development and implementation of Markov chain Monte Carlo methods for inferences for ion channel data, Laplace transform based inference for ion channel data and the development and analysis of models for interacting multiple channels.

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Title Optimal control in yield management
Group(s) Statistics and Probability
Proposer(s) Dr David Hodge
Description

Serious mathematics studying the maximization of revenue from the control of price and availability of products has been a lucrative area in the airline industry since the 1960s. It is particularly visible nowadays in the seemingly incomprehensible price fluctuations of airline tickets. Many multinational companies selling perishable assets to mass markets now have large Operations Research departments in-house for this very purpose. This project would be working studying possible innovations and existing practices in areas such as: customer acceptance control, dynamic pricing control and choice-based revenue management. Applications to social welfare maximization, away from pure monetary objectives, and the resulting game theoretic problems are also topical in home energy consumption and mass online interactions.

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Title Stochastic Processes on Manifolds
Group(s) Statistics and Probability
Proposer(s) Prof Huiling Le
Description

As well as having a wide range of direct applications to physics, economics, etc, diffusion theory is a valuable tool for the study of the existence and characterisation of solutions of partial differential equations and for some major theoretical results in differential geometry, such as the 'Index Theorem', previously proved by totally different means. The problems which arise in all these subjects require the study of processes not only on flat spaces but also on curved spaces or manifolds. This project will investigate the interaction between the geometric structure of manifolds and the behaviour of stochastic processes, such as diffusions and martingales, upon them.

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Title Statistical Theory of Shape
Group(s) Statistics and Probability
Proposer(s) Prof Huiling Le
Description

Devising a natural measure between any two fossil specimens of a particular genus, assessing the significance of observed 'collinearities' of standing stones and matching the observed systems of cosmic 'voids' with the cells of given tessellations of 3-spaces are all questions about shape.

It is not appropriate however to think of 'shapes' as points on a line or even in a euclidean space. They lie in their own particular spaces, most of which have not arisen before in any context. PhD projects in this area will study these spaces and related probabilistic issues and develop for them a revised version of multidimensional statistics which takes into account their peculiar properties. This is a multi-disciplinary area of research which has only become very active recently. Nottingham is one of only a handful of departments at which it is active.

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Title Automated tracking and behaviour analysis
Group(s) Statistics and Probability
Proposer(s) Dr Christopher Brignell
Description

In collaboration with the Schools of Computer and Veterinary Science we are developing an automated visual surveillance system capable of identifying, tracking and recording the exact movements of multiple animals or people.  The resulting data can be analysed and used as an early warning system in order to detect illness or abnormal behaviour.  The three-dimensional targets are, however, viewed in a two dimensional image and statistical shape analysis techniques need to be adapted to improve the identification of an individual's location and orientation and to develop automatic tests for detecting specific events or individuals not following normal behaviour patterns.

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Title Asymptotic techniques in Statistics
Group(s) Statistics and Probability
Proposer(s) Prof Andrew Wood
Description

Asymptotic approximations are very widely used in statistical practice. For example, the large-sample likelihood ratio test is an asymptotic approximation based on the central limit theorem. In general, asymptotic techniques play two main roles in statistics: (i) to improve understanding of the practical performance of statistics procedures, and to provide insight into why some proceedures perform better than others; and (ii) to motive new and improved approximations. Some possible topics for a Ph.D. are

  • Saddlepoint and related approximations
  • Relative error analysis
  • Approximate conditional inference
  • Asymptotic methods in parametric and nonparametric Bayesian Inference
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Title Statistical Inference for Ordinary Differential Equations
Group(s) Statistics and Probability
Proposer(s) Dr Theodore Kypraios, Dr Simon Preston, Prof Andrew Wood
Description

Ordinary differential equations (ODE) models are widely used in a variety of scientific fields, such as physics, chemistry and biology.  For ODE models, an important question is how best to estimate the  model parameters given experimental data.  The common (non-linear  least squares) approach is to search parameter space for parameter values that minimise the sum of squared differences between the model solution and the experimental data. However, this requires repeated numerical solution of the ODEs and thus is computationally expensive; furthermore, the optimisation's objective function is often highly multi-modal making it difficult to find the global optimum.  In this project we will develop computationally less demanding  likelihood-based methods, specifically by using spline regression  techniques that will reduce (or eliminate entirely) the need to solve numerically the ODEs.

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Title Statistical shape analysis with applications in structural bioinformatics
Group(s) Statistics and Probability
Proposer(s) Dr Christopher Fallaize
Description

In statistical shape analysis, objects are often represented by a configuration of landmarks, and in order to compare the shapes of objects, their configurations must first be aligned as closely as possible. When the landmarks are unlabelled (that is, the correspondence between landmarks on different objects is unknown) the problem becomes much more challenging, since both the correspondence and alignment parameters need to be inferred simultaneously.

An example of the unlabelled problem comes from the area of structural bioinformatics, when we wish to compare the 3-d shapes of protein molecules. This is important, since the shape of a protein is vital to its biological function. The landmarks could be, for example, the locations of particular atoms, and the correspondence between atoms on different proteins is unknown. This project will explore methods for unlabelled shape alignment, motivated by the problem of protein structure alignment. Possible topics include development of:
i) efficient MCMC methods to explore complicated, high-dimensional distributions, which may be highly multimodal when considering large proteins;
ii) fast methods for pairwise alignment, needed when a large database of structures is to be searched for matches to a query structure;
iii) methods for the alignment of multiple structures simultaneously, which greatly exacerbates the difficult problems faced in pairwise alignment.   

Relevant Publications
  • Green, P.J. and Mardia, K.V. (2006) Bayesian alignment using hierarchical models, with applications in protein bioinformatics. Biometrika, 93(2), 235-254.
  • Mardia, K.V., Nyirongo, V.B., Fallaize, C.J., Barber, S. and Jackson, R.M. (2011). Hierarchical Bayesian modeling of pharmacophores in bioinformatics. Biometrics, 67(2), 611-619.
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Title High-dimensional molecular shape analysis
Group(s) Statistics and Probability
Proposer(s) Prof Ian Dryden
Description

In many application areas it is of interest to compare objects
and to describe the variability in shape as an object evolves over time.
For example in molecular shape analysis it is common to have several thousand
atoms and a million time points. It is of great interest to reduce the
dimension to a relatively small number of dimensions, and to describe
the variability in shape and coverage properties over time. Techniques
from manifold learning will be explored, to investigate if the variability can
be effectively described by a low dimensional manifold. A recent method for
shapes and planar shapes called principal nested spheres will be adapted for
3D shape and surfaces. Also, other non-linear dimension reduction techniques such as
multidimensional scaling will be explored, which approximate the geometry
of the higher dimensional manifold. The project will involve collaboration
with Dr Charlie Laughton of the School of Pharmacy.

Relevant Publications
  • Jung, S., Dryden, I.L. and Marron, J.S. (2012). Analysis of principal nested spheres. Biometrika, 99, 551–568.
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Title Statistical analysis of neuroimaging data
Group(s) Statistics and Probability, Mathematical Medicine and Biology
Proposer(s) Dr Christopher Brignell
Description

The activity of neurons within the brain can be detected by function magnetic resonance imaging (fMRI) and magnetoencephalography (MEG).   The techniques record observations up to 1000 times a second on a 3D grid of points separated by 1-10 millimetres.  The data is therefore high-dimensional and highly correlated in space and time.  The challenge is to infer the location, direction and strength of significant underlying brain activity amongst confounding effects from movement and background noise levels.  Further, we need to identify neural activity that are statistically significant across individuals which is problematic because the number of subjects tested in neuroimaging studies is typically quite small and the inter-subject variability in anatomical and functional brain structures is quite large.

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Title Identifying fibrosis in lung images
Group(s) Statistics and Probability, Mathematical Medicine and Biology
Proposer(s) Dr Christopher Brignell
Description

Many forms of lung disease are characterised by excess fibrous tissue developing in the lungs.  Fibrosis is currently diagnosed by human inspection of CT scans of the affected lung regions.  This project will develop statistical techniques for objectively assessing the presence and extent of lung fibrosis, with the aim of identifying key factors which determine long-term prognosis.  The project will involve developing statistical models of lung shape, to perform object recognition, and lung texture, to classify healthy and abnormal tissue.  Clinical support and data for this project will be provided by the School of Community Health Sciences.

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Title Modelling hospital superbugs
Group(s) Statistics and Probability, Mathematical Medicine and Biology
Proposer(s) Prof Philip O'Neill, Dr Theodore Kypraios
Description

The spread of so-called superbugs such as MRSA within healthcare settings provides one of the major challenges to patient welfare within the UK. However, many basic questions regarding the transmission and control of such pathogens remain unanswered. This project involves stochastic modelling and data analysis using highly detailed data sets from studies carried out in hospital, addressing issues such as the effectiveness of patient isolation, the impact of different antibiotics, the way in which different strains interact with each other, and the information contained in data on high-resolution data (e.g. whole genome sequences).

Relevant Publications
  • Kypraios, T., O'Neill, P. D., Huang, S. S., Rifas-Shiman, S. L. and Cooper, B. S. (2010) Assessing the role of undetected colonization and isolation precautions in reducing Methicillin-Resistant Staphylococcus aureus transmission in intensive care units. BMC Infectious Diseases 10(29).
  • Worby, C., Jeyaratnam, D., Robotham, J. V., Kypraios, T., O.Neill, P. D., De Angelis, D., French, G. and Cooper, B. S. (2013) Estimating the effectiveness of isolation and decolonization measures in reducing transmission of methicillin-resistant Staphylococcus aureus in hospital general wards. American Journal of Epidemiology 177 (11), 1306-1313.
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Title Modelling of Emerging Diseases
Group(s) Statistics and Probability, Mathematical Medicine and Biology
Proposer(s) Prof Frank Ball
Description

When new infections emerge in populations (e.g. SARS; new strains of influenza), no vaccine is available and other control measures must be adopted. This project is concerned with addressing questions of interest in this context, e.g. What are the most effective control measures? How can they be assessed? The project involves the development and analysis of new classes of stochastic models, including intervention models, appropriate for the early stages of an emerging disease.

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Title Structured-Population Epidemic Models
Group(s) Statistics and Probability, Mathematical Medicine and Biology
Proposer(s) Prof Frank Ball
Description

The structure of the underlying population usually has a considerable impact on the spread of the disease in question. In recent years the Nottingham group has given particular attention to this issue by developing, analysing and using various models appropriate for certain kinds of diseases. For example, considerable progress has been made in the understanding of epidemics that are propogated among populations made up of households, in which individuals are typcially more likely to pass on a disease to those in their household than those elsewhere. Other examples of structured populations include those with spatial features (e.g. farm animals placed in pens; school children in classrooms; trees planted in certain configurations), and those with random social structure (e.g. using random graphs to describe an individual's contacts). Projects in this area are concerned with novel advances in the area, including developing and analysing appropriate new models, and methods for statistical inference (e.g. using pseudo-likelihood and Markov chain Monte Carlo methods).

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Title Bayesian Inference for Complex Epidemic Models
Group(s) Statistics and Probability, Mathematical Medicine and Biology
Proposer(s) Prof Philip O'Neill, Dr Theodore Kypraios
Description

Data-analysis for real-life epidemics offers many challenges; one of the key issues is that infectious disease data are usually only partially observed. For example, although numbers of cases of a disease may be available, the actual pattern of spread between individuals is rarely known. This project is concerned with the development and application of methods for dealing with these problems, and involves using the latest methods in computational statistics (e.g. Markov Chain Monte Carlo (MCMC) methods, Approximate Bayesian Computation, Sequential Monte Carlo methods etc).

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Title Bayesian model choice assessment for epidemic models
Group(s) Statistics and Probability, Mathematical Medicine and Biology
Proposer(s) Prof Philip O'Neill, Dr Theodore Kypraios
Description

During the last decade there has been a significant progress in the area of parameter estimation for stochastic epidemic models. However, far less attention has been given to the issue of model adequacy and assessment, i.e. the question of how well a model fits the data. This project is concerned with the development of methods to assess the goodness-of-fit of epidemic models to data, and methods for comparing different models.

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Title Epidemics on random networks
Group(s) Statistics and Probability, Mathematical Medicine and Biology
Proposer(s) Prof Frank Ball
Description

There has been considerable interest recently in models for epidemics on networks describing social contacts.  In these models one first constructs an undirected random graph, which gives the network of possible contacts, and then spreads a stochastic epidemic on that network.  Topics of interest include: modelling clustering and degree correlation in the network and analysing their effect on disease dynamics; development and analysis of vaccination strategies, including contact tracing; and the effect of also allowing for casual contacts, i.e. between individuals unconnected in the network.  Projects in this area will address some or all of these issues.

Relevant Publications
  • Ball F G and Neal P J (2008) Network epidemic models with two levels of mixing. Math Biosci 212, 69-87.
  • Ball F G, Sirl D and Trapman P (2009) Threshold behaviour and final outcome of an epidemic on a random network with household structure. Adv Appl Prob 41, 765-796.
  • Ball F G, Sirl D and Trapman P (2010) Analysis of a stochastic SIR epidemic on a random network incorporating household structure. Math Biosci 224, 53-73.
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Title Statistical analysis of fibre variability in composites manufacture
Group(s) Statistics and Probability, Scientific Computation
Proposer(s) Prof Frank Ball, Prof Michael Tretyakov
Description

Multidisciplinary collaborations are a critical feature of material science research enabling integration of data collection with computational and/or mathematical modelling. This PhD study provides an exciting opportunity for an individual to participate in a project spanning research into composite manufacturing, stochastic modelling, statistical analysis and scientific computing. The project is integrated into the EPSRC Centre for Innovative Manufacturing in Composites, which isled by the University of Nottingham and delivers a co-ordinated programme of research in composites manufacturing.

This project focuses on the development of a manufacturing route for composite materials capable of producing complex components in a single process chain based on advancements in the knowledge, measurement and prediction of uncertainty in processing. The outcome of this work will enable a step change in the capabilities of composite manufacturing technologies to be made, overcoming limitations related to part thickness, component robustness and manufacturability as part of a single process chain, whilst yielding significant developments in mathematics and statistics with generic application in the fields of stochastic modelling and inverse problems.

The specific aims of this project are: (i) statistical analysis of fibber placements based on textile and composite material data sets; (ii) statistical analysis and stochastic modelling of permeability of textiles and composites; (iii) efficient sampling techniques of stochastic permeability. A student will obtain an excellent grasp of various statistical and stochastic techniques (e.g., spatial statistical methods, use of random fields, Monte Carlo methods), how to apply them, how to work with real data and how to do related modelling and simulation. This knowledge and especially experience are transferable to other applications of statistics and probability.

The PhD programme contains a training element, the exact nature of which will be mutually agreed by the student and their supervisors.

We require an enthusiastic graduate with a 1st class honours in Mathematics (in exceptional circumstances a 2(i) class degree can be considered), preferably at the MMath/MSc level, with good programming skills and williness to work as a part of an interdisciplinary team. A candidate with a solid background in statistics and stochastic processes will have an advantage.

The studentship is available for a period of three and a half years from September/October 2015 and provides a stipend and full payment of Home/EU Tuition Fees. Students must meet the EPSRC eligibility criteria.

Informal enquiries should be addressed to Prof. Michael Tretyakov, email: michael.tretyakov@nottingham.ac.uk.

To apply, please access: https://my.nottingham.ac.uk/pgapps/welcome/. Please ensure you quote ref: SCI/1262x1. This studentship is open until filled. Early application is strongly encouraged.

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