Statistical ideas and tools are used in almost all employment sectors including banking/finance, government, medical research, the pharmaceutical industry and internet companies.
This one-year full-time programme provides outstanding training both in theoretical and applied statistics, with sufficient flexibility to allow you to develop your own specialist interests.
The course will equip you with a range of statistical skills, including problem-solving, project work and presentation, to enable you to take prominent roles in a wide spectrum of employment and research.
The course consists of compulsory courses to ensure that all students have broad knowledge and experience of basic statistical skills.
You can also choose eight optional courses which provide depth and exposure to the diverse range of statistical applications and methods. This allows you to specialise in a specific area of statistics.
A major project provides an opportunity to work extensively on either theoretical or practical problems. The entire Statistics section within the Department of Mathematics is involved in running the MSc. This allows a very wide choice of research projects. The Statistics Section also has strong links to the financial and industrial sectors. This means that some projects will be delivered in conjunction with an external partner organisation.
M5MS01 Probability for Statistics
Review of axiomatic probability theory: probability spaces, distributions and their characteristics [including generating functions], conditional distributions.
Asymptotic theorems and convergence. Convergence modes and stochastic orders, convergence of transformations, laws of large numbers, central limit theorem, martingales.
Multivariate normal distribution. Gaussian processes.
Markov chains. Markov processes, classification of chains, stationary distributions, continuous-time Markov chains.
M5MS02 Fundamentals of Statistical Inference
Comparison of conditional and unconditional power functions, weighing machine example. Approaches to inference: Bayesian, Fisherian, frequentist.
Decision theory: risk, criteria for a decision rule, minimax and Bayes rules, finite decision problems.
Bayesian methods: fundamental elements, choice of prior, general form of Bayes rules. Empirical Bayes, hierarchical modelling. Predictive distributions, shrinkage and James-Stein estimation.
Data reduction and special models. Exponential families, transformation models. Sufficiency and completeness. Conditionality and ancillarity.
Key elements of frequentist theory. Hypothesis testing: Neyman-Pearson, uniformly most powerful tests, two-sided tests, conditional inference and similarity. Optimal point estimation. Confidence sets.
Introduction to likelihood theory. Asymptotic properties of maximum likelihood estimators, testing procedures. Multiparameter problems.
M5MS03 Applied Statistics
Two class classification problem, with error-minimising decision boundaries from quadratic discriminant analysis and k-nearest neighbour.
Statistical Models and modelling illustrated with real examples.
Simple and multiple linear regression. Model diagnostics and iterative modelling. Handling messy data, such as missing values. Sparsity and Lasso.
Generalised linear models: logistic, log-linear.
Basic linear time series models, e.g. ARMA.
Multi-level models and repeated measures.
Classification and discrimination.
M5MS04 Computational Statistics
Illustration of a particle filter.
Statistical Computing: R programming: data structures, programming constructs, object system, graphics.
Numerical methods: root finding, numerical integration, optimisation methods such as EM-type algorithms.
Simulation: generating random variates, Monte Carlo integration.
Simulation approaches in inference: randomisation and permutation procedures, bootstrap, MCMC, Sequential Monte Carlo/particle filtering.
M5MS05 Advanced Statistical Theory
Multiple hypothesis testing in a genomic inference problem (Prof Young) This course aims to give an introduction to key developments in contemporary statistical theory, building on ideas developed in the core course Fundamentals of Statistical Inference. Reasons for wishing to extend the techniques discussed in that course are several. Optimal procedures of inference, as described, say, by Neyman-Pearson theory, may only be tractable in unrealistically simple statistical models. Distributional approximations, such as those provided by asymptotic likelihood theory, may be judged to be inadequate, especially when confronted with small data samples (as often arise in various fields, such as particle physics and in examination of operational loss in financial systems). It may be desirable to develop general purpose inference methods, such as those given by likelihood theory, to explicitly incorporate ideas of appropriate conditioning. In many settings, such as bioinformatics, we are confronted with the need to simultaneously test many hypotheses. More generally, we may be confronted with problems where the dimensionality of the parameter of the model increases with sample size, rather than remaining fixed.
We consider here a number of topics motivated by such considerations. Focus will be on developments in likelihood-based inference, but we will give consideration too to: problems of multiple testing, objective Bayes methods, bootstrap alternatives to analytic distributional approximation, and introduce too more theoretical notions involved in high-dimensional inference.
A Bayesian analysis of the spectrum of a very distant astronomical object known as a quasar. Bayesian methods allow us to draw inference under sophisticated models for complex physical phenomenon and depend fundamentally on the famous theorem of the Rev. Bayes. (Image credits: Top, Astrophysical Journal, 688, 807; Lower Left. CHANDRA X-ray Observatory CXC Operated for NASA by SAO).
M5MS06 Bayesian Data Analysis
(Prof van Dyk) Scientific inquiry is an iterative process of integrating and accumulating information. Investigators assess the current state of knowledge regarding the issue of interest, gather new data to address remaining questions, and then update and refine their understanding to incorporate both new and old data. Bayesian inference provides a logical, quantitative framework for this process. This framework is based fundamentally on the familiar theorem from basic probability theory known as Bayes' Theorem.
Although Bayesian statistical methods have long been of theoretical interest, the relatively recent advent of sophisticated computational methods such as Markov chain Monte Carlo has catapulted Bayesian methods to centre stage. We can now routinely fit Bayesian models that are custom made to describe the idiosyncratic complexities of particular data streams in a multitude of scientific, technological, and policy settings. The ability to easily develop customized statistical techniques has revolutionized our ability to handle complex data. Bayesian methods now play an important role in the analysis of data from Marketing and sales, online activity, security camera streams, transportation, climate and weather, medical records, bioinformatics, and a myriad of other human activities and physical processes. In this course we will develop tools for designing, fitting, validating, and comparing the highly structured Bayesian models that are so quickly transforming how scientists, researchers, and statisticians approach their data.
Comparison of the cubic smoothing spline using generalized cross-validation and wavelet smoothing using the universal threshold of a Doppler function with additive normal noise.
M5MS07 Non-parametric Smoothing and Wavelets
(Dr Missaoui) Kernel estimators: window width, adaptive kernel estimators.
Roughness penalties: Cubic splines; Spline smoothing, Reinsch algorithm; alternative penalties: lasso, ridge regression.
Basis function approach: B-spines, wavelets: discrete wavelet transform; wavelet filters; the maximal overlap discrete wavelet transform; wavelet variance, wavelet shrinkage, thresholding.
Generic Model choice: AIC, BIC, cross-validation.
M5MS08 Multivariate Analysis
(Dr Cohen) As the name indicates, multivariate analysis comprises a set of techniques dedicated to the analysis of data sets with more than one outcome variable. A situation that is ubiquitous across all areas of science. Multiple uses of univariate statistical analysis is insufficient in this settings where interdependency between the multiple random variables are of influence and interest. In this course we look at some of the key ideas associated with multivariate analysis. Topics covered include a comprehensive introduction to the linear algebra used in multivariate analysis and the standard multivariate notations including the Kronecker product, a detailed treatment of the multivariate normal distribution, the Wishart distribution, Hotelling’s T2 statistic, some key likelihood ratio tests and the ordinary, multiple and partial measures of correlation.
M5MS09 Graphical Models
Is heart disease gender dependent, among non-obese, non-smoking, active individuals?
(Prof Walden) Probabilistic graphical models encode the relationships between a set of random variables, in a manner that relies on networks and graph-theoretic intuitions. Primarily, they encode conditional independence assumptions, whereby A is statistically independent of B conditional on the value of C. Just as conditional probability is one of the pillars of modern probability, conditional independence is critical in statistical modelling. It underlies model specification, and allows us to infer, elicit, and understand correlation structures between unobserved variables, given the value s of variables we already know. This course will entail a variety of material, including discrete mathematics (graph theory), statistical modelling, algorithms and computational aspects, as well as applications, involving real da t a and actual applications . We will also touch upon abstract questions, such as the difference between causality a nd correlation.
A machine learning al gorithm identifies brain regions that discriminate between Alzheimer's disease patients and healthy individuals.
M5MS10 Machine Learning
(Dr Calderhead) The fields of machine learning and computational statistics are readily becoming important areas of general practice, research and development within the mathematical sciences. The associated methodology is finding application in areas as varied as biology, economics and geopetroleum engineering, and its growth can be partly explained by the increase in the quantity and diversity of measurements we are able to make in the world around us. Particularly fascinating examples arise in biology, where we are now able to measure changes in molecular concentrations within specific gene regulatory networks of an organism that would have been hard to imagine only a short time ago. Machine learning techniques are vital for the distillation of useful structure from this data while avoiding model overfitting; in particular they allow us to distinguish signal from noise and characterise the most plausible scientific hypotheses given the data and prior information available to us. Many other areas and application domains, from social network analysis to algorithmic trading, benefit from machine learning methods, which are routinely used for the detection of patterns and anomalies in large quantities of data.
M5MS11 Statistics for Extreme Events
Time series of major insurance claims due to fires in Denmark, 1980–1990 (Dr Veraart) This course introduces extreme value theory. We focus on statistical methods for extreme events and study applications in insurance and finance. The main topics are as follows:
Extreme value theory: Fluctuations of maxima; fluctuations of upper order statistics;
Statistical Methods: Probability and quantile plots; mean excess function; Gumbel’s method of exceedances; parameter estimation for the generalised extreme value distribution; estimating under maximum domain of attraction conditions; fitting excess over a threshold.
M5MS12 Financial Econometrics
(Dr Veraart) Financial econometrics is an interdisciplinary area focusing on a wide range of quantitative problems arising from finance. This course gives an introduction to the field and presents some of the key statistical techniques needed to deal with both low and high frequency financial data. Main topics of the course are:
Discrete time framework: ARCH, GARCH models and their estimation;
Continuous time framework: Brownian motion, stochastic integration and stochastic differential equations, Itô’s formula, stochastic volatility, realised quadratic variat ion and its asymptotic properties, Lévy processes, testing for jumps, volatility estimation in the presence of market microstructure effects.
M5MS13 Pricing and Hedging in Financial Markets
(Dr Pakkanen) The fundamentals of no-arbitrage theory and risk neutral valuation of contingent claims in the setting of the trinomial model will be explained. The most commonly traded contingent claims in the financial markets (vanilla and forward starting options, barrier and volatility derivatives, American options) will be described in detail and their pricing discussed in the context of trinomial models.
M5MS14 Statistical Bioinformatics and Genetics
Circos plot showing genome-wide DNA copy number aberrations and interactions from a study of colorectal cancer. (not running in 2014/15) Advances in biotechnology are making routine use of DNA sequencing and microarray technology in biomedical research and clinical use a reality. Innovations in the field of Genomics are not only driving new investigations in the understanding of biology and disease but also fuelling rapid developments in computer science, statistics and engineering in order to support the massive information processing requirements.
In this course, students will be introduced into the world of Bioinformatics which has become in the last 10-15 years one of the dominant areas of research and application for modern Statistics. Students will learn about fundamental biological processes, classical models that have enabled scientists to model and understand complex biological datasets, as well as cutting edge methodology currently being used in next generation sequencing technologies.
M5MS15 Statistics in Retail Finance
Expected Loss distributions, by Risk grade. Estimated using Monte Carlo simulation on Basel II formulae. (Dr Missaoui) Retail finance is a business sector that has used mathematical and statistical methods successfully for credit risk analysis and operational decision making for over 50 years. In this course we will cover credit scores and their use in credit application decision making. We will introduce the segmented logistic regression model as a standard model of credit scorecard development and consider industry standard methods for assessing the performance of these models such as the receiver-operating characteristics (ROC) curve and Gini coefficient.
Issues that are very specific to retail finance, such as sample selection bias and reject inference will be covered in some depth, along with methods for fraud detection. Behavioural models of credit usage using survival and Markov transition models will be studied. These can be used as the basis of calculations of expected profitability. This leads naturally to portfolio level models where estimates of profit or loss are required across portfolios of financial products. In particular, Value-at-Risk (VaR) and expected shortfall estimates are used for capital requirements calculations, and derive the Merton/Vasicek formula which forms the basis of capital requirements calculations in the international Basel Accord on banking. Finally, we consider statistical approaches to stress testing, using simulation based on portfolio-level credit risk models.
M5MS16 Principles of Bayesian Inference
An artist's conception of how ULAS J1120+0641, the most distant quasar ever discovered, might appear c l o s e up. This quasar was discovered by I mperial College astronomer s usin g B ayesian methods to identify it from a catalogue of 20 m il lion astronomical sources. Image Credit: Gemini Observatory/AURA by Lynette Cook.(Dr Mortlock) Everybody has to make inferences - and decisions - on the basis of incomplete information; Bayesian inference is a powerful and comprehensive way of approaching such problems.&a mp;am p;nbs p; ; This co u rse proceeds from the Cox proofs that Bayes's theorem follows from basic axioms and self-consistency requirements, and then moves through to the application of these principles to parameter estimation, model comparison and experimental design. Examples are taken from fields as diverse as gambling, medicine, economics and astrophysics. The latter is a particular focus as it is a quantitative physical science in which there is very limited control about what sort of data can be obtained; this relatively new field of "astrostatistics" is also an active area of research within the Statistics Section and Astrophysics Group at Imperial College.
M5MS17 Medical Statistics
Radiotelemetric collection of blood pressure data in a controlled experiment to assess the effectiveness of a new chemical compound.
(Dr Bottolo) The objective of the course is to provide a broad range of statistical techniques to analyse biomedical data that are produced by pharmaceutical companies, research units and the NHS. Besides a general introduction to linear, generalised linear models and survival analysis, the course will focus on clinical trials (study design, randomisation, sample size and power, covariates and subgroups adjustment) to examine the effect of treatments on the disease process over time and longitudinal data analysis from the perspective of clinical trials. The statistical theory and the derivation and estimation of model parameters will be illustrated as well as the application of longitudinal models on real case studies drawn from biomedical and health sciences. The analysis of the real examples will be performed using standard statistical software. At the end of the course, students will be able to plan basic clinical trials, analyze longitudinal data and interpret the results.
The course will cover the following models and topics:
- Introduction to linear/generalised linear models and survival analysis
- Introduction to clinical trials
- Treatment allocation, monitoring and effect estimation
- Introduction to longitudinal data and repeat measures
- General and generalised linear model for longitudinal data
- Random and mixed-effects models
M5MS18 Official Statistics
Repossession claims per 1,000 households, 2010 Q4 to 2011 Q3. Courtesy of the Guardian Datablog.(Dr Kantas) "Statistics are the mirror through which we view society" (David Hand). How can the well-being of a nation be measured? Has the UK been faring better than Europe during the financial crisis? Were the policies of our government succesful? Sound policy making must rely on evidence, and the task of gathering such evidence reliably across a multitude of individuals, social groups, businesses and types of activities, is monumental. This is an exciting time for official statistics: the raw data are increasingly becoming available for public scrutiny, and recent developments are redefining what constitutes "well-being", "progress", and how they can be measured.
M5MS19 Further Topics in Statistics
(Dr Kantas) This course covers varying current topics in Statistics. Change in residuals over time squaredWe will consider semi-parametric methods for continuous outcomes including weighted least squares and sandwich estimators of the variance. The course will also cover specification and estimation of covariances and inference, with a focus on linear mixed effect models and Generalized Estimating Equations (GEEs). Time permitting, the we will also be covered estimation in the presence of time-varying confounding and extensions to discrete data.
M5S14 Survival Models and Actuarial Applications with Advanced Study
Mortality curves for males and females in the UK between 2008-2010.(Mr Ginzberg) Survival analysis, also known as reliability analysis and event history analysis, is a branch of statistical theory concerned with modelling the random times at which specific events will occur, utilising any relevant information available. Since survival data occur temporally, survival analysis data sets will typically be incomplete, with a proportion of the observations censored since the event time has not yet occurred at the time of analysis.
The discipline has a wide variety of applications, with examples including: medicine, when measuring the time until recovery/relapse of a patient following a medical intervention; engineering, measuring the time until failure of components in a machine; economics, measuring the time until failure of businesses.
This course introduces the fundamental ideas and statistical tools for performing survival analysis, which are applicable to the range of applications indicated above. Further, we consider some more tailored statistical models which are specifically appropriate to the discipline of actuarial science, in which there is interest in measuring mortality in a population for the purpose of providing life assurance and pensions.
M5S8 Time Series with Advanced Study
Autocorrelation sequences illustrating short-memory behaviour (upper plot) and long-memory behaviour (lower plot). (Prof Walden) An introduction to the analysis of time series (series of observations, usually evolving in time) is given which gives weight to both the time domain and frequency dom ain viewpoints. Important structural features (e.g. reversibility) are discussed, and useful computational algorithms and approaches are introduced. The course is self-contained.
Discrete time stochastic processes and examples. ARMA processes. Trend removal and seasonal adjustment. General linear process. Invertibility. Directionality and reversibility in time series. Spectral representation. Aliasing. Generating functions. Estimation of mean and autocovariance sequence. The periodogram. Tapering for bias reduction. Parametric model fitting. Forecasting.
Additional material: From long-memory processes, Au toregr e ssive parametric spectrum estimation, Harmonic analysis, Mult icha nnel time series modelling and analysis.
Computational Stochastic Processes
(Dr Pavliotis) Stochastic processes play an increasingly important role in the model l in g of physical, chemical and biological systems. Most stochastic mathematical models are analytically intractable and have to be simulated on a computer. Th is course will introduce basic numerical and computational techniques for simulating stochastic processes and will present applications to specific physical problems. Contents include:
Simulation of Brownian motion, Brownian bridge, geometric Brownian motion.
Simulation of random fields, The Karhunen-Loeve expansion.
Numeri cal methods for stochastic differential equations, weak and strong convergence, stability, numerical simulation of ergodic SDEs.
Backward/forward Kolmogorov equations. Numerical methods for parabolic PDEs (finite difference, spectral methods).
Calculation of the transition probability density and of the invariant measure for ergodic diffusion processes.
Statistical inference for diffusion processes, maximum likelihood, method moments.
Markov Chain Monte Carlo, sampling from probability distributions.
Applications: computational statistical mechanics, molecular dynamics
Assessment: This course is examined entirely by projects.
Mastery Material: Extension within the scope of the projects.
Prerequisites: stochastic processes (at the level of Applied Stochastic Processes M5A42), ODEs, PDEs, linear algebra, scientific computing, numerical analysis. Knowledge of matlab or any other programming language.
Universities in the United Kingdom use a centralized system of undergraduate application: University and College Admissions Service (UCAS). It is used by both domestic and international students. Students have to register on the UCAS website before applying to the university. They will find all the necessary information about the application process on this website. Some graduate courses also require registration on this website, but in most cases students have to apply directly to the university. Some universities also accept undergraduate application through Common App (the information about it could be found on universities' websites).
Both undergraduate and graduate students may receive three types of responses from the university. The first one, “unconditional offer” means that you already reached all requirements and may be admitted to the university. The second one, “conditional offer” makes your admission possible if you fulfill some criteria – for example, have good grades on final exams. The third one, “unsuccessful application” means that you, unfortunately, could not be admitted to the university of you choice.
All universities require personal statement, which should include the reasons to study in the UK and the information about personal and professional goals of the student and a transcript, which includes grades received in high school or in the previous university.
The minimum qualifications for admission are a degree of class 2i or higher, or equivalent, in Statistics, Mathematics or a related subject, such as Engineering or Physics.
There is no GMAT requirement.
We cannot comment on the eligibility of applicants without seeing a full application form along with references and transcripts.
Successful applicants must be able to meet all conditions of their offer, including the language requirement, before the course begins.
The Andrew Jennings Scholarship
Student Status Eligibility - Open pre-enrolment only
Value - £2,000 towards maintenance costs
Number Available - 1
Further Eligibility Criteria Information
The Andrew Jennings Scholarship is awarded by DecisionMetrics in the memory of a founding member, Andrew Jennings. DecisionMetrics is a credit risk analytics business and this award is intended for a student who has an interest in retail credit risk.
This award is open to all Home/UK and EU applicants who have been made an offer to study an MSc in Statistics degree within the Department of Mathematics at Imperial College London, starting in October 2015.
Application Deadline Date 31-MAR-2015
To apply please submit a short essay entitled "Why I am interested in credit scoring", which should be no more than one A4 page in length, to the Department of Mathematics by 31 March 2015. Your essay will be used along with your admission application and references to assess your academic merit and potential.
You must have received an offer to study an MSc degree in Statistics by 31 March 2015.
Applications will be ranked within the Department of Mathematics and the scholar demonstrating the most academic potential will receive the award.
Outcome of the Award
The successful applicant will be notified by email no later than 1 June 2015. If you have not received confirmation of an award by this date please assume you have been unsuccessful in your application.
9. Agreeing to these terms and conditions and supplying your UK bank details
a) All scholarship and bursary payments will be made to the UK bank account details held on your Student e-Service account. You are able to log into your Student e-Service account and make changes to your bank details at any time after you’ve accepted your admissions offer.
b) By submitting your bank details via the Student Funding tab in Imperial’s Student e-Service portal, and/or bursary form, you are confirming that you agree with the terms and conditions of the award.
c) It may take a few weeks to set up your bursary payments and your UK bank account (if applicable); therefore you should bring sufficient funds to cover your living expenses during this time. Initial payment dates may vary; it is your responsibility to ensure you are aware of when payments will be made.
d) The award is subject to you fulfilling any outstanding conditions of admission.
e) Funds will only be released in line with your registration at College and you will need to ensure your bank details are up to date.
f) Payment Dates: Payments are normally made on the 7th day of each month; bank details should be updated before the 24th day of the preceding month to ensure payment is not delayed. Undergraduate payments will commence from 7th November. Postgraduate payments will commence on the 7th of the month following your registration.
10. Please make sure that you have completed all the steps necessary to register for the academic year in which you wish to receive payment. Please note that new award holders will also need to have fulfilled all of their conditions of offer before they are able to register.
11. All Imperial scholarships are subject to satisfactory academic progression. If the duration of your scholarship is longer than 12 months, it will be renewable annually.
12. Awards will not generally be made to those already holding a full scholarship from another source; please inform Student Financial Support, and/or any other department which has offered you an award, immediately if you are granted more than one award, even if you have already accepted our award. If you wish to hold several partial awards concurrently, this will be considered on a case-by-case basis.
13. Scholarships are not generally awarded to students who are writing-up.
14. Applicants wishing to study at UK partner institutions are not eligible for Imperial College London scholarships.
15. Undergraduate Financial Support / Imperial Bursary Package
a) To be eligible to receive an Imperial Bursary you must have been assessed for means tested funding from Student Finance England (or equivalent funding authority) and have a household income below the Imperial household income threshold for your cohort. You must contact us if this is not the case. Any previous study may affect your entitlement.
b) The College reviews household income information (which it receives from Student Finance England, etc.) on a continuous basis. A change in your household income may result in a change in your Imperial Bursary. Any overpayments will be reclaimed.
c) The Imperial Bursary is available for each year of your course excluding repeat years of study and NHS funded years for Medical courses. If you change from a 3 year to a 4 year course at Imperial you will be awarded a further year’s bursary. You should contact us about any course changes as soon as possible.
d) Students on paid placements might not be eligible for the Imperial Bursary.
e) To be eligible for the Imperial Bursary, we must receive your household income from the Student Loans Company by 1 May following the start of your academic year.
16. If you have been offered funding by the Research Councils, please ensure that you have read the most up-to-date postgraduate funding guide; you will need to adhere to the terms and conditions laid out there.
17. Deferrals, withdrawals and interruption of studies
a) You must inform the Student Financial Support team immediately of any interruptions to your study, particularly if they are likely to affect your attendance and registration status at College.
b) If you withdraw from your course or take an interruption of study (IOS) you must notify us immediately by contacting us here. If you take an IOS your bursary will be postponed until you re-register.
c) Bursaries and scholarships are not transferable. If you transfer to another institution or withdraw from the College, any payments due to you will be cancelled and any overpayments are recoverable.
d) We will not provide scholarship or bursary support for any period of repeat study.
e) Awards cannot be deferred.
18. Student Financial Support may at any time, at their discretion, withdraw or recover an award for breach of any of the above conditions.
19. The College reserves the right to place a limit on financial support where a student is in receipt of other funding.
20. Information on students is shared within the Imperial College community and donors (where applicable and relevant to your award) in accordance with the Data Protection Act 1998.
a) Where awards have specific eligibility criteria (e.g. satisfactory academic progression), supporting evidence may be shared with named donors in order to verify continued eligibility.
b) Award recipients may be expected to meet with donors.
21. If you are in receipt of an award to study that is restricted to students on the basis of nationality or residency; please note that, in accordance with the Equality Act 2010, you must not intend to exercise in Great Britain skills you have obtained as a result of your training at the College and you must not be ordinarily resident in an EEA state.
22. These terms and conditions are the formal rules which regulate centrally funded awards. As such, there are no appeal procedures associated with funding from the Student Financial Support team.
This award is for students starting in the academic year 2015-16 and cannot be deferred.
Tuition fees (2015–2016):