Students preparing for their graduation ceremony at Canterbury Cathedral

International Master's in Statistics with Finance - MSc

2018

This programme, accredited by the Royal Statistical Society (RSS), equips aspiring professional statisticians with the skills they will need for posts in industry, government, research and teaching. It is suitable preparation too for careers in other fields requiring a strong statistical background.

2018

Overview

Students whose mathematical and statistical background is insufficient for direct entry on to the appropriate programme, may apply for this course. The first year of the programme gives you a strong background in statistics, including its mathematical aspects, equivalent to the Graduate Diploma in Statistics. This is followed by the MSc in Statistics with Finance.

About the School of Mathematics, Statistics and Actuarial Science (SMSAS)

The School has a strong reputation for world-class research and a well-established system of support and training, with a high level of contact between staff and research students. Postgraduate students develop analytical, communication and research skills. Developing computational skills and applying them to mathematical problems forms a significant part of the postgraduate training in the School. We encourage all postgraduate statistics students to take part in statistics seminars and to help in tutorial classes.

The Statistics Group is forward-thinking, with varied research, and received consistently high rankings in the last two Research Assessment Exercises.

Statistics at Kent provides:

  • a programme that gives you the opportunity to develop practical, mathematical and computing skills in statistics, while working on challenging and important problems relevant to a broad range of potential employers
  • teaching and supervision by staff who are research-active, with established reputations and who are accessible, supportive and genuinely interested in your work
  • advanced and accessible computing and other facilities
  • a congenial work atmosphere with pleasant surroundings, where you can socialise and discuss issues with a community of other students.

National ratings

In the Research Excellence Framework (REF) 2014, research by the School of Mathematics, Statistics and Actuarial Science was ranked 25th in the UK for research power and 100% or our research was judged to be of international quality.

An impressive 92% of our research-active staff submitted to the REF and the School’s environment was judged to be conducive to supporting the development of world-leading research.

Course structure

Linear algebra, analysis, regression and probability and inference are core topics for the first year of this two-year programme, which also includes a dissertation module. In the second year, stochastic models and processes, Bayesian statistics and the analysis of large data sets are among the range of topics explored.

Modules

The following modules are indicative of those offered on this programme. This list is based on the current curriculum and may change year to year in response to new curriculum developments and innovation.  Most programmes will require you to study a combination of compulsory and optional modules. You may also have the option to take modules from other programmes so that you may customise your programme and explore other subject areas that interest you.

Modules may include Credits

This module covers aspects of Statistics which are particularly relevant to insurance. Some topics (such as risk theory and credibility theory) have been developed specifically for actuarial use. Other areas (such as Bayesian Statistics) have been developed in other contexts but now find applications in actuarial fields. Stochastic processes of events such as accidents, together with the financial flow of their payouts underpin much of the work. Since the earliest games of chance, the probability of ruin has been a topic of interest. Outline Syllabus includes: Decision Theory; Bayesian Statistics; Loss Distributions; Reinsurance; Credibility Theory; Empirical Bayes Credibility theory; Risk Models; Ruin Theory; Generalised Linear Models; Run-off Triangles.

Marks on this module can count towards exemption from the professional examination CT6 of the Institute and Faculty of Actuaries. Please see http://www.kent.ac.uk/casri/Accreditation/index.html for further details.

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A stochastic process is a process developing in time according to probability rules, for example, models for reserves in insurance companies, queue formation, the behaviour of a population of bacteria, and the persistence (or otherwise) of an unusual surname through successive generations.The syllabus will include coverage of a wide variety of stochastic processes and their applications: Markov chains; processes in continuous-time such as the Poisson process, the birth and death process and queues.

Marks on this module can count towards exemption from the professional examination CT4 of the Institute and Faculty of Actuaries. Please see http://www.kent.ac.uk/casri/Accreditation/index.html for further details.

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A time series is a collection of observations made sequentially in time. Examples occur in a variety of fields, ranging from economics to engineering, and methods of analysing time series constitute an important area of statistics. This module focuses initially on various time series models, including some recent developments, and provides modern statistical tools for their analysis. The second part of the module covers extensively simulation methods. These methods are becoming increasingly important tools as simulation models can be easily designed and run on modern PCs. Various practical examples are considered to help students tackle the analysis of real data.The syllabus includes: Difference equations, Stationary Time Series: ARMA process. Nonstationary Processes: ARIMA Model Building and Testing: Estimation, Box Jenkins, Criteria for choosing between models, Diagnostic tests.Forecasting: Box-Jenkins, Prediction bounds. Testing for Trends and Unit Roots: Dickey-Fuller, ADF, Structural change, Trend-stationarity vs difference stationarity. Seasonality and Volatility: ARCH, GARCH, ML estimation. Multiequation Time Series Models: Spectral Analysis. Generation of pseudo – random numbers, simulation methods: inverse transform and acceptance-rejection, design issues and sensitivity analysis.

Marks on this module can count towards exemption from the professional examination CT6 of the Institute and Faculty of Actuaries. Please see http://www.kent.ac.uk/casri/Accreditation/index.html for further details.

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Multivariate normal distribution, Inference from multivariate normal samples, principal component analysis, mixture models, factor analysis, clustering methods, discrimination and classification, graphical models, the use of appropriate software.

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Probability: Joint distributions of two or more discrete or continuous random variables. Marginal and conditional distributions. Independence. Properties of expectation, variance, covariance and correlation. Poisson process and its application. Sums of random variables with a random number of terms.

Transformations of random variables: Various methods for obtaining the distribution of a function of a random variable —method of distribution functions, method of transformations, method of generating functions. Method of transformations for several variables. Convolutions. Approximate method for transformations.

Sampling distributions: Sampling distributions related to the Normal distribution — distribution of sample mean and sample variance; independence of sample mean and variance; the t distribution in one- and two-sample problems.

Statistical inference: Basic ideas of inference — point and interval estimation, hypothesis testing.

Point estimation: Methods of comparing estimators — bias, variance, mean square error, consistency, efficiency. Method of moments estimation. The likelihood and log-likelihood functions. Maximum likelihood estimation.

Hypothesis testing: Basic ideas of hypothesis testing — null and alternative hypotheses; simple and composite hypotheses; one and two-sided alternatives; critical regions; types of error; size and power. Neyman-Pearson lemma. Simple null hypothesis versus composite alternative. Power functions. Locally and uniformly most powerful tests. Composite null hypotheses. The maximum likelihood ratio test.

Interval estimation: Confidence limits and intervals. Intervals related to sampling from the Normal distribution. The method of pivotal functions. Confidence intervals based on the large sample distribution of the maximum likelihood estimator – Fisher information, Cramer-Rao lower bound. Relationship with hypothesis tests. Likelihood-based intervals.

In addition, for level 6 students:

Bayesian Inference: Prior and posterior distributions, conjugate prior, loss function, Bayesian estimators and credible intervals. Examples of application.

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Simple linear regression; the method of least squares; sums of squares; the ANOVA table; residuals and diagnostics; matrix formulation of the general linear model; prediction; variable selection; one-way analysis of variance; practical regression analysis using software; logistic regression (level 6 only).

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This modules offer students the opportunity to work on a project in statistics or probability. Student choose a project and supervisor during the Autumn term and work on the project with the support of the supervisor in the Spring term. The module offers the opportunity to develop their skills in self-study and report writing.

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This module is a sequel to Algebraic Methods. It considers the abstract theory of linear spaces together with applications to matrix algebra and other areas of Mathematics (and its applications). Since linear spaces are of fundamental importance in almost every area of mathematics, the ideas and techniques discussed in this module lie at the heart of mathematics.

Topics covered will include:

1 Vector Spaces: definition, examples, linearly independent and spanning sets, bases, dimension, subspaces.

2 Linear transformations: definition, examples, matrix of a linear transformation, change of basis, similar matrices.

3 Determinant of a linear transformation.

4 Eigenvalues/eigenvectors and diagonalisation: characteristic polynomial, invariant subspaces and upper triangular forms. Cayley-Hamilton Theorem.

5 Bilinear forms: inner products, norms, Cauchy-Schwarz inequality.

6 Orthonormal systems, the Gram-Schmidt process.

7 Symmetric Matrices. Every real symmetric matrix is diagonalisable.

8 Quadratic forms: Sylvester's Law of Inertia; signature of a quadratic form; application to conics (and quadrics if time permits).

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Topics covered will include:

Real Numbers: Rational and real numbers, absolute value and metric structure on the real numbers, induction, countability and uncountability, infimum and supremum.

Limits of Sequences: Sequences, definition of convergence, epsilon terminology, uniqueness, algebra of limits, comparison principles, standard limits, subsequences and non-existence of limits, convergence to infinity.

Completeness Properties: Cantor's Intersection Theorem, limit points, Bolzano-Weierstrass theorem, Cauchy sequences.

Continuity of Functions: Functions and basic definitions, limits of functions, continuity and epsilon terminology, sequential continuity, Intermediate Value Theorem.

Differentiation: Definition of the derivative, product rule, quotient rule and chain rule, derivatives and local properties, Mean Value Theorem, L'Hospital's Rule.

Taylor Approximation: Taylor's Theorem, remainder term, Taylor series, standard examples, O and o notation, limits using Taylor series.

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Multivariate normal distribution, Inference from multivariate normal samples, principal component analysis, mixture models, factor analysis, clustering methods, discrimination and classification, graphical models, the use of appropriate software.

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An investor needs an assortment of tools in their toolkit to weigh up risk and return in alternative investment opportunities. This module introduces various measures of investment risk and optimal investment strategies using modern portfolio theory. Pricing of assets using the classical capital asset pricing model and arbitrage pricing theory are discussed. The theory of Brownian motion is used to analyse the behaviour of the lognormal model of asset prices, which is then compared with the auto-regressive Wilkie model of economic variables and asset prices. Principles of utility theory, behavioural finance and efficient market hypothesis provide the context from an investor's perspective. Outline syllabus includes: Measures of investment risk, Mean-Variance Portfolio Theory, Capital Asset Pricing Model, Arbitrage Pricing Theory, Brownian Motion, Lognormal Model, Wilkie Model, Utility Theory and Stochastic Dominance, Efficient Market Hypothesis and Behavioural Finance.

Marks on this module can count towards exemption from the professional examination CT8 of the Institute and Faculty of Actuaries. Please see http://www.kent.ac.uk/casri/Accreditation/index.html for further details.

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15

A stochastic process is a process developing in time according to probability rules; for example, models for reserves in insurance companies, queue formation, the behaviour of a population of bacteria, and the persistence (or otherwise) of an unusual surname through successive generations. The module will focus on the idea of a stochastic process, and show how this notion can be combined with probability and matrix to build a stochastic model. It will include coverage of a wide variety of stochastic processes and their applications; random walk; Markov chains; processes in continuous-time such as the Poisson process, the birth and death process and Brownian motion; renewal processes; queues; branching processes; epidemic models.

Marks on this module can count towards exemption from the professional examination CT4 of the Institute and Faculty of Actuaries. Please see http://www.kent.ac.uk/casri/Accreditation/index.html for further details.

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15

This module introduces the main features of basic financial derivative contracts and develops pricing techniques. Principle of no-arbitrage, or absence of risk-free arbitrage opportunities, is applied to determine prices of derivative contracts, within the framework of binomial tree and geometric Brownian motion models. The interplay between pricing and hedging strategies, along with risk management principles, are emphasized to explain the mechanisms behind derivative instruments. Models of interest rate and credit risk are also discussed in this context.  Outline syllabus includes: An introduction to derivatives, binomial tree model, Black-Scholes option pricing formula, Greeks and derivative risk management, interest rate models, credit risk models.

Marks on this module can count towards exemption from the professional examination CT8 of the Institute and Faculty of Actuaries. Please see http://www.kent.ac.uk/casri/Accreditation/index.html for further details.

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The module, which is compulsory for students of MSc in Statistics and MSc in Statistics with Finance, enables students to undertake an independent piece of work in a particular area of statistics, or statistical finance/financial econometrics and to write a coherent account of the material. A list of possible topics, together with names of Staff willing to supervise these projects, will be circulated to students in the autumn term. A broad range of projectsis available, encompassing both practical data analysis and more methodological work, although projects that are primarily theoretical will typically have obvious practical applications. Students then choose a topic after consultation and agreement with the relevant member of staff. This is done early in the spring term and some preliminary work is done during the spring term, leading to a short presentation at the end of that term. The main part of the project is then undertaken after the examinations in May.

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This module begins by introducing probability, primarily as a tool that underlies the subsequent material on statistical inference. This includes, for example, various notions of convergence for random variables. Classical statistical inference assumes that data follow a probability model with some unknown parameters, and the main aims are to estimate these parameters and to test hypotheses about them. The focus of the module is to develop general methods of statistical inference that can be applied to a wide range of problems. Outline syllabus includes: probability axioms; marginal, joint and conditional distributions; Bayes theorem; important distributions; convergence of random variables; sampling distributions; likelihood; point estimation; interval estimation; likelihood-ratio, Wald and score tests; estimating equations.

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This module covers regression techniques used to understand the effect of explanatory variables on a response, which may be continuous, ordinal or categorical. Issues including general inference, goodness-of-fit, variable selection and diagnostics will be discussed and the material presented in a data-centred way. Outline Syllabus includes: Linear Model: Simple and multiple linear regression including inference (estimation, hypothesis testing and confidence intervals) and diagnostics (detection of outliers, multicollinearity and influential observations). The General linear model, polynomial regression and analysis of variance. Discrete data analysis: Review of Binomial, Poisson, negative binomial and multinomial distributions. Properties, estimation, hypothesis tests. Generalized Linear Model: Estimation, hypothesis testing and model comparison of these models. Diagnostics and goodness-of-fit. Contingency tables: Tests for independence, Measures of association, logistic models, multidimensional tables, log linear models, fitting and model selection.

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15

The origins of Bayesian inference lie in Bayes' Theorem for density functions; the likelihood function and the prior distribution combine to provide a posterior distribution which reflects beliefs about an unknown parameter based on the data and prior beliefs. Statistical inference is determined solely by the posterior distribution. So, for example, an estimate of the parameter could be the mean value of the posterior distribution. This module will provide a full description of Bayesian analysis and cover popular models, such as the normal distribution. Initially, the flavour will be one of describing the Bayesian counterparts to well known classical procedures such as hypothesis testing and confidence intervals. Current methods for inference involving posterior distributions typically involve sampling strategies. That is, due to the complicated nature of some posterior distributions, analytic methods fail to provide meaningful summaries. Hence, sampling from the posterior has become popular. A full description of sampling techniques, starting from rejection sampling, will be given. Outline Syllabus includes: Conjugate models (prior and posterior belong to the same family of parametric models). Predictive distributions; Bayes estimates; Sampling density functions; Gibbs and Metropolis-Hastings samplers; Winbugs; Bayesian regression and hierarchical models; Bayesian model choice; Decision theory; Objective priors; Exchangeability.

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Nonparametric Methods: This part of the module comprises approximately 10 lectures on nonparametric methods, showing how they are applied in practice for testing goodness of fit to a distribution, including tests of normality, for testing randomness of a sequence, and for comparing two samples. Practical Statistics: There is no fixed syllabus for this component of the course. Students gain experience of practical data analysis through a series of assessments that confront them with unfamiliar data, which may require the use of techniques introduced in any of the other core modules of the Programme. Statistical Computing: At the start of the module, students are introduced to, and gain experience of, the document preparation system LaTeX, which enables the production of high-quality mathematical documents. Then there are sessions in which students learn the statistical package R, using a mixture of lectures and hands-on computing workshops. The initial aim is for students to gain familiarity with importing and manipulating data, producing graphs and tables, and running standard statistical analyses. The later parts of the module focus on the use of R as a programming language, introducing basic programming mechanisms such as loops, conditional statements and functions. This provides students with the means to develop their own code to undertake non-routine types of analysis if these are not already available in R.

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Teaching and Assessment

The programme is assessed by coursework and written examinations. In the second year, there is also a substantial dissertation.

Programme aims

This programme aims to:

  • give you the depth of technical appreciation and skills appropriate to Masters’ level
  • students in statistics
  • equip you with a comprehensive and systematic understanding of theoretical and
  • practical statistics, and their uses in finance
  • develop your capacity for rigorous reasoning and precise expression
  • develop your capability to formulate and solve problems relevant to statistics
  • develop your appreciation of recent developments in statistics and the links
  • between the theory of statistics and financial modelling (and other areas of application)
  • develop your logical, mathematical approach to solving problems
  • develop your enhanced capacity for independent thought and work
  • ensure you are competent in the use of information technology, and are familiar
  • with computers and relevant software
  • provide you with opportunities to study advanced topics in statistics, engage in research at some level, and develop communication and personal skills
  • provide you with the depth of knowledge of the subject sufficient to enter a career as a professional statistician or appropriate career in quantitative finance
  • provide a deep understanding of the use of statistics in finance and financial  econometrics.

Learning outcomes

Knowledge and understanding

You will gain knowledge and understanding of:

  • probability and statistics and the range of principles involved
  • the links between different statistical concepts and methods
  • advanced information technology skills relevant to statisticians
  • a comprehensive range of methods and techniques appropriate to statistics at postgraduate level
  • the role of logical mathematical argument and deductive reasoning
  • an appreciation of particular subject areas to which statistics is applied, particularly finance, and the important role of statistics in those areas
  • an appreciation of the use of statistics in finance and the probabilistic concepts involved.

Intellectual skills

You develop intellectual skills in:

  • the ability to demonstrate a comprehensive understanding of the main body of statistical knowledge
  • the ability to demonstrate skill in calculation and manipulation of data
  • the ability to apply a range of statistical concepts and principles in various challenging contexts
  • the ability for logical argument
  • the ability to demonstrate skill in solving complex statistical problems using appropriate and advanced methods
  • the ability in relevant computer skills and usage
  • the ability to work with relatively little guidance
  • the ability to evaluate research work critically.

Subject-specific skills

You gain subject-specific skills in:

  • the ability to demonstrate knowledge of advanced statistical concepts and topics, both explicitly and by applying them to the solution of problems
  • the ability to demonstrate knowledge of statistical modelling techniques commonly applied to finance
  • the ability to abstract the essentials of problems to facilitate statistical analysis and interpretation
  • the ability to present statistical analyses and draw conclusions with clarity and accuracy.

Transferable skills

You will gain the following transferable skills:

  • problem-solving skills: the ability to work independently to solve problems involving qualitative or quantitative information
  • communication skills, including the capacity to report to others on analyses undertaken
  • computational skills
  • information-retrieval skills involving a range of resources
  • information technology skills including scientific word-processing
  • time-management and organisational skills, as evidenced by the ability to plan and implement efficient and effective modes of working
  • skills needed for continuing professional development.

Careers

Students often go into careers as professional statisticians in industry, government, research and teaching but our programmes also prepare you for careers in other fields requiring a strong statistical background. You have the opportunity to attend careers talks from professional statisticians working in industry and to attend networking meetings with employers.

Recent graduates have started careers in diverse areas such as the pharmaceutical industry, financial services and sports betting.

Professional recognition

The taught programmes in Statistics and Statistics with Finance provide exemption from the professional examinations of the Royal Statistical Society and qualification for Graduate Statistician status.

Study support

Postgraduate resources

Kent’s Computing Service central facility runs Windows. Within the School, postgraduate students can use a range of UNIX servers and workstations. Packages available include R, SAS, MATLAB, SPSS and MINITAB.

Dynamic publishing culture

Staff publish regularly and widely in journals, conference proceedings and books. Among others, they have recently contributed to: Annals of Statistics; Biometrics; Biometrika; Journal of Royal Society, Series B; Statistics and Computing. Details of recently published books can be found within our staff research interests.

Global Skills Award

All students registered for a taught Master's programme are eligible to apply for a place on our Global Skills Award Programme. The programme is designed to broaden your understanding of global issues and current affairs as well as to develop personal skills which will enhance your employability.  

Entry requirements

A good first degree (or the equivalent) in an appropriate quantitative subject.

All applicants are considered on an individual basis and additional qualifications, and professional qualifications and experience will also be taken into account when considering applications. 

International students

Please see our International Student website for entry requirements by country and other relevant information for your country. 

English language entry requirements

The University requires all non-native speakers of English to reach a minimum standard of proficiency in written and spoken English before beginning a postgraduate degree. Certain subjects require a higher level.

For detailed information see our English language requirements web pages. 

Need help with English?

Please note that if you are required to meet an English language condition, we offer a number of pre-sessional courses in English for Academic Purposes through Kent International Pathways.

Research areas

Biometry and ecological statistics

Specific interests are in biometry, cluster analysis, stochastic population processes, analysis of discrete data, analysis of quantal assay data, overdispersion, and we enjoy good links within the University, including the School of Biosciences and the Durrell Institute of Conservation and Ecology. A recent major joint research project involves modelling the behaviour of yeast prions and builds upon previous work in this area. We also work in collaboration with many external institutions.

Bayesian statistics

Current work includes non-parametric Bayes, inference robustness, modelling with non-normal distributions, model uncertainty, variable selection and functional data analysis.
Bioinformatics, statistical genetics and medical statistics Research covers bioinformatics (eg DNA microarray data), involving collaboration with the School of Biosciences. Other interests include population genetics, clinical trials and survival analysis.

Nonparametric statistics

Research focuses on empirical likelihood, high-dimensional data analysis, nonlinear dynamic analysis, semi-parametric modelling, survival analysis, risk insurance, functional data analysis, spatial data analysis, longitudinal data analysis, feature selection and wavelets.

Staff research interests

Full details of staff research interests can be found on the School's website.

Dr Diana Cole: Senior Lecturer in Statistics

Branching processes in biology; cell division models; ecological statistics; generalised linear mixed models; identifiability.; parameter redundancy.

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Dr Alfred Kume: Senior Lecturer in Statistics

Shape analysis; directional statistics; image analysis.

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Dr Alexa Laurence: Lecturer in Statistics

Medical statistics and applied statistics.

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Dr Fabrizio Leisen: Senior Lecturer in Statistics

Bayesian nonparametrics; MCMC, Urn models; Markov and Levy processes; Move-to-Front and Move-to-Root allocation rules.

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Dr Owen Lyne: Lecturer in Statistics

Stochastic epidemic models; applied probability; simulation; statistical inference; goodness of fit; branching processes; martingales; medical education.

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Professor Byron Morgan: Professor of Applied Statistics

Biometry; cluster analysis; stochastic population processes; psychological applications of statistics; multivariate analysis; simulation; analysis of quantal assay data; medical statistics; ecological statistics; overdispersion; estimation using transforms. 

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Dr Rachel McCrea: Research Associate

Integrated population modelling of dependent data structures.

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Professor Martin S Ridout: Professor of Applied Statistics

Analysis of discrete data in biology; generalised linear models; overdispersion; stochastic models; transform methods.

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Dr Xue Wang: Lecturer in Statistics

Bayesian nonparametric methods; copula function with its applications in finance; wavelet estimation methods.

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Professor Jian Zhang: Professor of Statistics

Semi and non-parametric statistical modelling; statistical genetics with medical applications; Bayesian modelling; mixture models; neuroimaging.

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Fees

The 2018/19 annual tuition fees for this programme are:

International Masters in Statistics with Finance - MSc at Canterbury:
UK/EU Overseas
Full-time N/A £15200

For students continuing on this programme fees will increase year on year by no more than RPI + 3% in each academic year of study except where regulated.* If you are uncertain about your fee status please contact information@kent.ac.uk

General additional costs

Find out more about general additional costs that you may pay when studying at Kent. 

Funding

Search our scholarships finder for possible funding opportunities. You may find it helpful to look at both: