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Matthew Lloyd Thomas

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SAMBa

Hello, I’m Matthew (or Matt) and I’m a postgraduate student at the University of Bath. I am currently working towards a PhD as part of the EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa CDT). I work under the supervision of Prof. Gavin Shaddick.
My primary research interests are spatial and spatio-temporal statistics and the implementation of Bayesian hierarchical models with large datasets. My PhD research involves developing Bayesian hierarchical models to integrate data from multiple (and often disparate) sources to estimate global air quality and the associated burden of disease. Alongside my PhD, I have been involved in a number of other short term projects centred in environment and health with collaborators such as the World Health Organization (WHO) and the Department of Pharmacy & Pharmacology at the University of Bath.
Prior to my PhD, I obtained a BSc in Mathematics and Statistics (2010-2014) and an MRes in Statistical Applied Mathematics (2014-2015) both at the University of Bath. As part of my undergraduate degree course I did a placement year, where I was a Statistical Programmer working with clinical trial data in the pharmaceutical company Roche.
An up-to-date CV can be found here.

Talks/Posters

Teaching

Department of Mathematical Sciences
University of Bath
Bath,
BA2 7AY
United Kingdom
Office: 4 West 3.38
Email: M.L.Thomas@bath.ac.uk

Publications

Submitted
Shaddick, G., Thomas, M. L., Amini, H., Broday, D., Cohen, A., Frostad, J., Green, A., Gumy, S., Liu, Y,. Martin, R., Prüss-Üstün, A., Simpson, D., van Donkelaar, A., & Brauer, M. Data integration for the assessment of population exposure to ambient air pollution for global burden of disease assessment.
Morrison, K. T., Shaddick, G., Thomas, M. L., Buckeridge, D. L. & Henderson, S. B. Improving forecast accuracy in environmental public health surveillance: a spatio-temporal approach.
Published
Shaddick, G., Thomas M. L., Jobling A., Brauer M., van Donkelaar, A., Burnett, R., Chang H., Cohen A., Van Dingenen, R., Dora, C., Gumy, S., Liu, Y., Martin, R., Waller, L. A., West, J., Zidek, J. V. and Prüss-Üstün A. (2018). Data Integration Model for Air Quality: A Hierarchical Approach to the Global Estimation of Exposures to Ambient Air Pollution. Journal of the Royal Statistical Society: Series C (Applied Statistics), 67(1), pp.231-253 (Link)
Gakidou, E., Afshin, A., Abajobir A. A., Abate, K. H., Abbafati, C., ..., Thomas, M. L., et al. (2017) Global, regional, and national comparative risk assessment of 84 behavioural, environmental and occupational, and metabolic risks or clusters of risks, 1990–2016: a systematic analysis for the Global Burden of Disease Study 2016. The Lancet 390: 1345-1422. (Link)
Cohen, A., Brauer, M., Burnett, R., Anderson, H. R., Frostad, J., Estep, K., Balakrishnan, K., Brunekreef, B., Dandona, L., Dandona, R., Feigin, V., Freedman, G., Hubbell, B., Haidong, K., Jobling, A., Knibbs, L., Liu, Y., Martin, R., Morawska, L., Pope, C., A., Shin, H., Straif, K., Shaddick, G., Thomas, M., van Dingenen, R., van Donkelaar, A., Vos, T., Murray, C. J. L. and Forouzanfar, M. H. (2017). The Global Burden of Disease attributable to ambient air pollution: Estimates of current burden and 25-year trends from the GBD2015 study. The Lancet 389: 1907-1918. (Link)
Tillett, W., Shaddick, G., Jobling, A., Askari, A., Cooper, A., Creamer, P., Clunie, G., Helliwell, P. S., James, J., Kay, L., Korendowych, E., Lane S., Packham, J., Shaban, R., Thomas, M., Williamson, L. and McHugh, N. (2016). Effect of anti-TNF and conventional synthetic disease-modifying anti-rheumatic drug treatment on work disability and clinical outcome in a multicentre observational cohort study of psoriatic arthritis. Rheumatology 56(4): 603-612. (Link)
Forouzanfar, M. H., Afshin, A., Alexander, L. T., Anderson, H. R., ..., Thomas, M. L., et al. (2016) Global, regional, and national comparative risk assessment of 79 behavioural, environmental and occupa- tional, and metabolic risks or clusters of risks, 1990–2015: a systematic analysis for the Global Burden of Disease Study 2015. The Lancet 388: 1659-1724. (Link)
Conference Contributions (peer reviewed)
Tillett, W., Shaddick, G., Jobling, A., Thomas, M. L., Korendowych, E., & McHugh, N. (2015). OP0001 Work Disability After Initiation of Anti-TNF and DMARD Treatment in Psoriatic Arthritis; Investigator LED, UK, Multicentre Observational Cohort Study (LOPAS II). Annals of the Rheumatic Diseases, 74(Suppl 2): 64-64.

Here is a list of publications that I have co-authored. Feel free to get in contact should you have any questions about these publications.

Publications

I don’t currently have any teaching commitments. Here is a list of tutorials, short-courses and workshops I have taught on previously,

TutorialsSpring Semester 2016/17: Quantitative Methods (MA10214), University of Bath.Winter Semester 2016/17: Business Data Analysis (MA10213), University of Bath.Winter Semester 2015/16: Business Data Analysis (MA10213), University of Bath.Short-Courses and WorkshopsFeb 2018: Statistical Methods and Data Analysis for Global Health. Imperial College London, UKNov 2017: Environmental Health Impact Assessment using R. Institute of Occupational Medicine, Edinburgh, Scotland.Aug 2017: Quantifying the Health Impacts of Air Pollution. BUCX (Bath-UNAM-CIMAT) Conference, UNAM, Mexico.Feb 2017: EU Cost Action, Industrially Contaminated Sites and Health Network (ICSHNet). Thessaloniki, Greece.Dec 2016: Bayesian Hierarchical Models. Latin American Congress of Probability and Mathematical Statistics (CLAPEM), Universidad de Costa Rica, Costa Rica.Nov 2016: Data Science and Statistics in Research: Unlocking the Power of your Data. International Research Collaboration Initiative (IRCI), National University of Mongolia, Mongolia.Oct 2016: Integrated environment and health impact assessment (IEHIA): A tool for inter-sectoral action. Tallinn, Estonia.Jul 2016: Integrated environment and health impact assessment (IEHIA): A tool for inter-sectoral action. Bucharest, Romania.Jun 2016: New Frontiers: Advanced Modelling in Space and Time. BUC4 (Bath-UNAM-CIMAT) Conference, University of Bath, UK.Feb 2016: Thinking Globally: The Role of Big Data. BUC2 (Bath-UNAM-CIMAT) Conference, UNAM, Mexico.Nov 2015: When Populations and Hazards Collide: Modelling Exposures and Health Risks. BUC1 (Bath-UNAM-CIMAT) Conference, CIMAT, Mexico.

Poster: GEOMED Conference 2017, Porto, Portugal
Title: Data Integration for high-resolution continental-scale estimation of air pollution concentrations
Date: 7th - 9th September 2017
Abstract: Air pollution represents one of the most important environmental risk factors to human health with a number of pollutants associated with adverse health outcomes. Epidemiological studies designed to estimate the risks associated with air pollution require accurate measures of concentrations with comprehensive coverage of a study area. Traditionally, these have been based on measurements from ground monitors but this may not provide information of sufficient quality and coverage to allow accurate spatial (and temporal) prediction at any location at which estimated concentrations are required. Ground monitoring data may therefore need to be supplemented with information from other sources, such as estimates from satellite remote sensing, chemical transport models, land use and topography. Set within a Bayesian hierarchical modelling framework, downscaling models are used to align data generated at different geographical resolutions, including point locations and a series of (potentially non-aligned) grids of varying resolutions. The proposed modelling approach is used to predict concentrations of nitrogen dioxide, together with measures of uncertainty, at a high-resolution throughout Western Europe by integrating data from ground monitoring, chemical transport models together with land-use information. Performing complex Bayesian inference combining potentially large datasets may be computationally challenging and we perform approximate Bayesian inference using INLA.
Talk: BUCX Conference, UNAM, México
Title: Data Integration for high-resolution continental-scale estimation of air pollution concentrations
Date: 9th August 2017
Abstract: Air pollution represents one of the most important environmental risk factors to human health with a number of pollutants associated with adverse health outcomes. Epidemiological studies designed to estimate the risks associated with air pollution require accurate measures of concentrations with comprehensive coverage of a study area. Traditionally, these have been based on measurements from ground monitors but this may not provide information of sufficient quality and coverage to allow accurate spatial (and temporal) prediction at any location at which estimated concentrations are required. Ground monitoring data may therefore need to be supplemented with information from other sources, such as estimates from satellite remote sensing, chemical transport models, land use and topography. Set within a Bayesian hierarchical modelling framework, downscaling models are used to align data generated at different geographical resolutions, including point locations and a series of (potentially non-aligned) grids of varying resolutions. The proposed modelling approach is used to predict concentrations of nitrogen dioxide, together with measures of uncertainty, at a high-resolution throughout Western Europe by integrating data from ground monitoring, chemical transport models together with land-use information. Performing complex Bayesian inference combining potentially large datasets may be computationally challenging and we perform approximate Bayesian inference using INLA.
Talk: SAMBa Summer Conference 2017
Title: Data Integration Model for Air Quality: A Hierarchical Approach to the Global Estimation of Exposures to Ambient Air Pollution
Date: 20th - 21st June 2017
Abstract: Calculating the burden of disease attributed to air pollution requires accurate estimation of population level exposures to pollutants. Although coverage of ground monitoring networks is increasing, these data are insufficient to independently estimate exposures globally. Information from other sources, such as satellite retrievals, chemical transport models and land use covariates must therefore be used in combination with ground monitoring data. Each of these data sources will have their own biases and uncertainties that may vary over space. Set within a Bayesian hierarchical modelling framework, the recently developed Data Integration Model for Air Quality (DIMAQ) integrates data from multiple sources and allows spatially-varying relationships between ground measurements and other factors that estimate fine particulate matter (PM2.5) concentrations. The outputs of the model are estimated exposures that can be combined with population estimates to produce population-level distributions of exposures for each country. DIMAQ was used to estimate exposures of PM2.5, together with associated measures of uncertainty, on a high-resolution grid (~11 km × 11 km) covering the entire globe for use in the 2016 WHO report ‘Ambient air pollution: A global assessment of exposure and burden of disease’, and in the 2015 and 2016 updates of the Global Burden of Disease. For 2015, 92% of the world’s population lived in areas that exceeded the WHO 10 µg/m3 guideline. Fifty percent of the global population resided in areas with PM2.5 concentrations above the WHO Interim Target 1 (IT-1 of 35 µgm-3); 64% lived in areas exceeding IT-2 (25 µgm-3); and 81% lived in areas exceeding IT-3 (15 µgm-3). Nearly all (86%) of the most extreme concentrations (above 75 µgm-3) were experienced by populations in China, India, Pakistan, and Bangladesh.
Talk: High Perfomance Computing (HPC) Conference 2017
Title: Global Estimation of Air Quality
Date: 12th June 2017
Abstract: Calculating the burden of disease attributed to air pollution requires accurate estimation of population level exposures to pollutants. Although coverage of ground monitoring networks is increasing, these data are insufficient to independently estimate exposures globally. Information from other sources, such as satellite retrievals, chemical transport models and land use covariates must therefore be used in combination with ground monitoring data. Each of these data sources will have their own biases and uncertainties that may vary over space. Set within a Bayesian hierarchical modelling framework, the recently developed Data Integration Model for Air Quality (DIMAQ) integrates data from multiple sources and allows spatially-varying relationships between ground measurements and other factors that estimate fine particulate matter (PM2.5) concentrations. The outputs of the model are estimated exposures that can be combined with population estimates to produce population-level distributions of exposures for each country. DIMAQ was used to estimate exposures of PM2.5, together with associated measures of uncertainty, on a high-resolution grid (~11 km × 11 km) covering the entire globe for use in the 2016 WHO report ‘Ambient air pollution: A global assessment of exposure and burden of disease’, and in the 2015 and 2016 updates of the Global Burden of Disease. For 2015, 92% of the world’s population lived in areas that exceeded the WHO 10 µg/m3 guideline. Fifty percent of the global population resided in areas with PM2.5 concentrations above the WHO Interim Target 1 (IT-1 of 35 µgm-3); 64% lived in areas exceeding IT-2 (25 µgm-3); and 81% lived in areas exceeding IT-3 (15 µgm-3). Nearly all (86%) of the most extreme concentrations (above 75 µgm-3) were experienced by populations in China, India, Pakistan, and Bangladesh.
Poster: Latin American Congress of Probability and Mathematical Statistics (CLAPEM) Conference, San Jose, Costa Rica
Title: Data Integration Model for Air Quality: A Hierarchical Approach to the Global Estimation of Exposures to Ambient Air Pollution
Date: 5th - 9th December 2016
Abstract: Air pollution is a major risk factor for global health, with an estimated 3 million deaths annually being attributed to ambient fine particulate matter (PM2.5). The primary source of information for estimating exposures to PM2.5 has been measurements from ground monitoring networks but, although coverage is increasing, there remain regions in which monitoring is limited. Ground monitoring data therefore needs to be supplemented with information from other sources, such as satellite retrievals of aerosol optical depth and chemical transport models. A hierarchical modelling approach for integrating data from multiple sources is proposed allowing spatially-varying relationships between ground measurements and other factors that estimate air quality. Set within a Bayesian framework, the resulting Data Integration Model for Air Quality (DIMAQ) is used to estimate exposures, together with associated measures of uncertainty, on a high resolution grid covering the entire world. Bayesian analysis on this scale can be computationally challenging and here approximate Bayesian inference is performed using Integrated Nested Laplace Approximations.
Poster: Latin American Congress of Probability and Mathematical Statistics (CLAPEM) Conference, San Jose, Costa Rica
TitleTrends in country-level exposures to particulate matter air pollution
Date 5th- 9th December 2016
Abstract: Exposure to ambient air pollution is a major risk factor for global disease. Assessment of the impacts of air pollution on population health and evaluation of trends factors requires accurate estimates of exposures experienced by populations. The recently developed Data Integration Model for Air Quality (DIMAQ) uses estimates from satellite retrievals of aerosol optical depth and chemical transport models, population density estimates, and topography, and calibrates them with ground monitoring data in order to provide estimates of exposures to PM2.5 at a high spatial resolution (10km x 10km) globally. Based on summaries of the posterior distributions for each grid cell, it is estimated that 92% of the world's population reside in areas exceeding the World Health Organization's Air Quality Guidelines. DIMAQ was also used to produce global estimates of annual average fine particle (PM2.5) for five-year intervals from 1990 to 2010 and yearly from 2011-2015. These estimates are used to examine trends in population exposures toPM2.5 for each of 184 countries.
Talk: RSC Conference 2016
Title: Global modelling of air pollution using multiple data sources
Date: 14th - 16th June 2016
Abstract: Air pollution is an important determinant of health and poses a significant threat globally. The World Health Organisation (WHO) are at the forefront of health modelling and policy development worldwide and must ensure that this is based on accurate and convincing evidence. A coherent framework for integrating data from various sources is required that provides accurate and effective analysis and yield exposure estimates with associated uncertainty. These estimates should be consistent with raw data and provide a means for explanation when there are discrepancies. I will explore the current methodology used within WHO to estimate air pollution levels and how changes in framework can significantly improve model predictions. I will also explain how Bayesian melding can be used to match the requirements for air pollution modelling within WHO and the associated challenges that arise from using this technique.
Talk: SAMBa ITT4: Health
Title: Techniques for Imputing Data Missing Not at Random
Date: 6th-10th June 2016
As part of SAMBa, students are required to attend workshops called Integrative Think Tanks (ITTs). These events bring academic, industrial, and other external partners to present problems requiring research solutions, in which students are encouraged and trained to form mathematical questions and potential solutions from Industrial problems. SAMBa students are required to present the progress from these workshops throughout the week. Here are some of the talks that I have given during these events:
Talk: Numerical Analysis Seminar
Title: The Numerical Analysts Guide to Approximate Bayesian Inference
Date: 8th April 2016
Abstract: Recently, there has been increased focus on performing approximate Bayesian inference, often using Integrated Nested Laplace Approximations (INLA), particularly with large-scale problems. While this may be computationally more attractive alternative to methods such as Markov Chain Monte Carlo, there are still issues that need to be addressed. During this talk I will explain what INLA is, why it's important and some of the interesting challenges in Numerical Linear Algebra that will need addressing in the future.
Talk: BUC2 Conference UNAM México
Title: Global modelling of air pollution using multiple data sources
Date: 24th February 2016
Abstract: Air pollution is an important determinant of health and poses a significant threat globally. The World Health Organisation (WHO) are at the forefront of health modelling and policy development worldwide and must ensure that this is based on accurate and convincing evidence. A coherent framework for integrating data from various sources is required that provides accurate and effective analysis and yield exposure estimates with associated uncertainty. These estimates should be consistent with raw data and provide a means for explanation when there are discrepancies. I will explore the current methodology used within WHO to estimate air pollution levels and how changes in framework can significantly improve model predictions. I will also explain how Bayesian melding can be used to match the requirements for air pollution modelling within WHO and the associated challenges that arise from using this technique.
Talk: BUC1 Conference CIMAT México
Title: Global modelling of air pollution using multiple data sources
Date: 11th November 2015
Abstract: Air pollution is an important determinant of health and poses a significant threat globally. The World Health Organisation (WHO) are at the forefront of health modelling and policy development worldwide and must ensure that this is based on accurate and convincing evidence. A coherent framework for integrating data from various sources is required that provides accurate and effective analysis and yield exposure estimates with associated uncertainty. These estimates should be consistent with raw data and provide a means for explanation when there are discrepancies. I will explore the current methodology used within WHO to estimate air pollution levels and how changes in framework can significantly improve model predictions. I will also explain how Bayesian melding can be used to match the requirements for air pollution modelling within WHO and the associated challenges that arise from using this technique.
Talk: Bath IMI Launch
Title: How an Industrial Placement Influenced Me
Date: 28th October 2015
Talk: SAMBa MRes Transfer Day
Title: Global modelling of air pollution using multiple data sources
Date: 5th November 2015
Abstract: Air pollution is an important determinant of health and poses a significant threat globally. The World Health Organisation (WHO) are at the forefront of health modelling and policy development worldwide and must ensure that this is based on accurate and convincing evidence. A coherent framework for integrating data from various sources is required that provides accurate and effective analysis and yield exposure estimates with associated uncertainty. These estimates should be consistent with raw data and provide a means for explanation when there are discrepancies. I will explore the current methodology used within WHO to estimate air pollution levels and how changes in framework can significantly improve model predictions. I will also explain how Bayesian melding can be used to match the requirements for air pollution modelling within WHO and the associated challenges that arise from using this technique.
Talk: SAMBa ITT2: Energy
Title 1: Spatio-Temporal Effects of Electricity Load Forecasting (1)
Title 2: Spatio-Temporal Effects of Electricity Load Forecasting (2)
Date: 1st-5th June 2015
As part of SAMBa, students are required to attend workshops called Integrative Think Tanks (ITTs). These events bring academic, industrial, and other external partners to present problems requiring research solutions, in which students are encouraged and trained to form mathematical questions and potential solutions from Industrial problems. SAMBa students are required to present the progress from these workshops throughout the week.
Talk: Student Led Symposium: Semester 2
Title: Quantile Regression estimation and Simplex Method
Date: 11th June 2015
As part of SAMBa, students are required to attend a seminar series called Student-Led Symposium (SLS). Topics in the SLS are steered to relate to upcoming Integrative Think Tanks (ITTs). Academic staff and industrial partners that attend the ITTs will be involved in the symposia series. SAMBa students are required to present at least once a semester in the first year. Students from later years will present developing research to first-year students, including open research problems for discussion.
Talk: SAMBa ITT1: Networks
Title 1: Bayesian Networks - QRA in DNV (1)
Title 2: Bayesian Networks - QRA in DNV (2)
Date: 26th-30th January 2015
As part of SAMBa, students are required to attend workshops called Integrative Think Tanks (ITTs). These events bring academic, industrial, and other external partners to present problems requiring research solutions, in which students are encouraged and trained to form mathematical questions and potential solutions from Industrial problems. SAMBa students are required to present the progress from these workshops throughout the week.
Talk: Student Led Symposium: Semester 1
Title: Monte Carlo Methods in Bayesian Statistics
Date: 4th December 2014
As part of SAMBa, students are required to attend a seminar series called Student-Led Symposium (SLS). Topics in the SLS are steered to relate to upcoming Integrative Think Tanks (ITTs). Academic staff and industrial partners that attend the ITTs will be involved in the symposia series. SAMBa students are required to present at least once a semester in the first year. Students from later years will present developing research to first-year students, including open research problems for discussion.

Talks/Posters

Here is a list and accompanying PDFs of talks and posters that I have presented. Feel free to get in contact should you have any questions about these talks.

May 2018
I was lucky enough to work in collaboration with the World Health Organisation (WHO) in order to produce the a set of population exposures and the burden of disease associated with ambient fine particulate matter (PM2.5) air pollution in 2016.
The WHO webpage for ambient air pollution and the associate burden of disease can be found here and an interactive map with the high-resolution gridded estimates can be found here.
This work also featured widely in the press during May 2018, and a select number of articles can be found below.
World Health Organization - 9 out of 10 people worldwide breathe polluted air, but more countries are taking action
University of Exeter - Nine out of 10 people worldwide breathe polluted air, new data shows
The i News - Revealed: The map that shows most of us are living in areas with ‘unsafe’ air pollution - This one I am particularly proud of as they feature a map that I created using R.
BBC News - UK's most polluted towns and cities revealed
The Guardian - Air pollution inequality widens between rich and poor nations
Daily Mail - Government urged to take action amid `worrying´ air pollution levels across UK
airqualitynews.com - WHO links 7 million deaths to particulate pollution
CNN - Which cities face most, least air pollution according to new WHO data
September 2016
I was lucky enough to work in collaboration with the World Health Organisation (WHO) in order to produce a set of population exposures and the burden of disease associated with ambient fine particulate matter (PM2.5) air pollution in 2016.
The WHO webpage for ambient air pollution and the associate burden of disease can be found here.
This work also featured widely in the press during September 2016, and a select number of articles can be found below.
World Health Organisation - WHO releases country estimates on air pollution exposure and health impacts
University of Bath - Outdoor air pollution exceeds WHO limits for 90% of UK population
SAMBa CDT - SAMBa newsletter January 2017
BBC News - Polluted air affects 92% of global population, says WHO.
Guardian - China tops WHO list for deadly outdoor air pollution
Daily Mail - How polluted is YOUR country? Interactive map reveals the worst places for toxic air that kills six million worldwide every year

News

Here is where I will place links to recent news articles/press releases which has featured the research that I work on.

Countries I have visited: Canada, China, Costa Rica, Croatia, Estonia, France, Germany, Greece, Ireland, Latvia, Mexico, Mongolia, Portugal, Romania, Spain, Switzerland, United Kingdom.

Before starting my PhD, I had only gone to very stereotypical locations British holidaymakers go on. I went to France and Spain a lot as well as travelling to a few locations across England and Wales. I am privileged enough that my PhD research has taken me all over. I have been to conferences and had meetings in countries that I wouldn’t have thought I would ever have visited in my life. These travels have led to really interesting cuisines, seen many famous landmarks and met some really interesting people. I blog about some of my experiences below.

Blog

My Travels

Blog Coming Soon.

SAMBa Reading List

Core Material
This list comprises of areas within Mathematics that are core to core to the SAMBa mandatory units. All students should consider the level of preparation and prior exposure they currently have in these areas before entering SAMBa.Numerics and Computation
Students need to have done an introductory course on Numerical Analysis/Matlab. Before entering SAMBa, students should be familiar with the following topics (although some of these will be reviewed in the courses):Basic MATLAB Programming for Numerical Analysis.Floating point numbers and rounding error.Concepts of Convergence and Accuracy: Order of convergence, extrapolation and error estimation.Approximation of Functions: Polynomial interpolation, error analysis.Integration: Newton-Cotes formulae. Gauss quadrature. Composite formulae. Error analysis.ODEs: Euler, Backward Euler, Trapezoidal and explicit Runge-Kutta methods. Stability and convergence.Linear Algebra: Gaussian elimination, LU decomposition, pivoting, Matrix norms, conditioning, backward error analysis, iterative refinement.The list below contains good references for this introductory material:Moler, Numerical Computing with Matlab (Link)Atkinson, An Introduction to Numerical Analysis , Wiley.Süli and Mayers, An Introduction to Numerical Analysis , Cambridge University Press.Iserles, A First Course in the Numerical Analysis of Differential Equations , Cambridge University Press.The above books cover more than is needed. In addtion the list below are the references which are used during the core SAMBa courses:Golub and Van Loan, Matrix Computations , Johns Hopkins University Press.Demmel, Applied Numerical Linear Algebra , SIAM.Trefethen and Bau, Numerical Linear Algebra , SIAM.Statistics
Before entering SAMBa, students should be familiar with the following topics in statistics:Hypothesis testing.Maximum likelihood estimation.Properties of multivariate normal random variables.The central limit theorem.Linear models.Generalised linear models.The SAMBa core unit MA40198 - Applied Statistical Inference is based on the textbook Core Statistics, which is available here. This book is an attempt to cover the minimum that a starting Ph.D. student in statistics should know. It contains a terse review of the prerequisite topics above, as well as the R language for statistical computing, which will be used in computer practicals. A student who is happy with everything in Core Statistics would be in very good shape for the statistical component of SAMBa.
Alternatively, books covering prerequisite material include the followingDalgaard, Introductory Statistics with R, Springer Science & Business MediaFaraway, Linear Models with R, CRC PressFaraway, Extending the Linear Models with R, CRC PressFor students with a strong interest in statistics, the following books contain material that is useful for Applied Statistical Inference, and a great deal more besides.Davison, Statistical Models, Cambridge University Press.Gelman et al., Bayesian Data Analysis, Chapman & Hall/CRC.Held and Bove - Applied Statistical Inference, Springer.Students who find this material challenging are advised to look at lecture notes from courses given by the Department of Mathematical Sciences, which will go at a slower pace to some of the literature above. To obtain these lecture notes, please email M.L.Thomas@bath.ac.ukAdditional Material
This list comprises of other areas within Mathematics that a SAMBa student may follow but are not core to any of the SAMBa mandatory units. Depending on the path through SAMBa that the student envisages, they should consider the level of preparation and prior exposure that they currently have in the following broad areas.Probability
Basic combinatorics, independence, random variables, discrete and continuous probability distributions, multivariate Normal distribution, law of large numbers, central limit theorem, conditional probability, conditional expectation, Markov processes, basic measure theory. Reading material includes:Ross, A First Course in Probability (9th ed.), Pearson.Grimmet and Stirzaker, Probability and Random Processes (3rd ed.), Oxford. (Relevant Chapters: 1 and 6.1-6.11)Williams, Probability with Martingales, Cambridge University Press. (For an introduction to measure-theoretic probability. Relevant Chapters: 0-6)Bartle, The Elements of Integration and Lebesgue Measure, Wiley (For those with no measure-theoretical background. Relevant Chapters: 1-6.)For those interested in taking MA50251 - Applied Stochastic Differential Equations in their first year should ensure that they read and are familiar with the following prerequisite material in probability:MA50251 Prerequisite MaterialPartial Differential Equations
Solution methods for Laplace’s equation, the heat equation and the wave equation in simple geometries in one, two and three space dimensions. Dirichlet and Neumann boundary conditions. Green’s functions. Fourier series solutions. Fourier and Laplace Transforms. Reading material includes:Pinchover and Rubinstein, An Introduction to Partial Differential Equations , Cambridge University Press.Strauss, Partial Differential Equations: An Introduction , WileyDynamical Systems
Linear ODEs, stability and classification of equilibrium points. Stable, unstable and centre manifolds. Codimension-one bifurcations (saddle-node, Hopf) of equilibria. Periodic orbits, Poincaré. maps, bifurcations of periodic orbits. Global bifurcations. Lyapunov exponents and chaos. Reading material includes:Glendinning, Stability, Instability and Chaos, Cambridge University Press.Strogatz, Nonlinear Dynamics and Chaos, Perseus Books, Cambridge, MA.Some more advanced texts are:Guckenheimer and Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (later edition), Springer.Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer.Mathematical Biology
Population dynamics of one or more species in discrete and continuous time, infectious diseases, population genetics, biological motion, molecular and cellular biology, pattern formation in biological systems, and tumour modelling. Reading material includes:Britton, Essential Mathematical Biology, Springer.Fluid Mechanics and Geophysical Flows
Streamlines and particle paths. Euler and Navier-Stokes equation for incompressible flow. Reynolds number. Streamfunctions. Vorticity. Invisicid flows and Bernoulli’s equation. Potential flow (e.g. around a cylinder) and Stokes flow. Boundary layers. Reading material includes:Acheson, An introduction to fluid dynamics, Oxford University Press.

The following reading lists will hopefully be useful for all incoming SAMBa students. They have been put together in order to summarise material that is either needed as a prerequisite for the courses on SAMBa or that will be used within the SAMBa courses.Copies of all of the books are available in the SAMBa student offices.