Students preparing for their graduation ceremony at Canterbury Cathedral

International Master's in Statistics - MSc


The International Master’s in Statistics develops your practical, statistical and computing skills to prepare you for a professional career in statistics or as a solid basis for further research in the area.



The programme has been designed to provide a deep understanding of the modern statistical methods required to model and analyse data. You will benefit from a thorough grounding in the ideas underlying these methods and develop your skills in key areas such as practical data analysis and data modelling.

It has been accredited by the Royal Statistical Society (RSS) and equips aspiring professional statisticians with the skills they need for posts in industry, government, research and teaching. It also enables you to develop a range of transferable skills that are attractive to employers within the public and private sectors.

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.

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.


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.

Possible modules may include Credits ECTS Credits

This module will consider many concepts you know from Calculus and put them on a more rigorous basis. The concept of a limit is basic to Calculus and, unless this concept is defined precisely, uncertainties and paradoxes will creep into the subject. Based on the foundation of the real number system, this module develops the theory of convergence of sequences and series and the study of continuity and differentiability of functions. The notion of Riemann integration is also explored. The syllabus includes the following: Sequences and their convergence. The convergence of bounded increasing sequences. Series and their convergence: the comparison test, the ratio test, absolute and conditional convergence, the alternating series test. Continuous functions: the boundedness theorem, the Intermediate Value Theorem. Differentiable functions: The Mean Value Theorem with applications, power series, Taylor expansions. Construction and properties of the Riemann integral.

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Systems of linear equations appear in numerous applications of mathematics. Studying solution sets to such systems leads to the abstract notions of a vector space and a linear transformation. Matrices can be used to represent linear transformations and to do concrete calculations. This module is about the properties of vector spaces, linear transformations and matrices. The syllabus includes: vector spaces, linearly independent and spanning sets, bases, dimension, subspaces, linear transformations, the matrix of a linear transformation, similar matrices, the determinant, diagonalisation, bilinear forms, norms, and the Gram-Schmidt process.

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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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Regression is a fundamental technique of statistical modelling, in which we aim to model a response variable using one or more explanatory variables. For example, we might want to model the yield of a chemical process in terms the temperature and pressure of the process. The need for statistical modelling arises because even when temperature and pressure are fixed, there will typically be variation in the resulting yield, so the model must include a random component. In this module we study the broad class of linear regression models, which are widely used in practice. We learn how to formulate such models and fit them to data, how to make predictions with associated measures of uncertainty, and how to select appropriate explanatory variables. Both theory and practical aspects are covered, including the use of computer software for regression. Through directed reading, students will also explore logistic regression models that are applicable when the response variable can take just two possible values. Outline of the syllabus: 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.

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ONLY AVAILABLE TO INTERNATIONAL MASTERS STUDENTS: This module is a pre-requisite for many of the other statistics modules at Stages 1 and 2, but it can equally well be studied as a module in its own right. It starts by revising the idea of a probability distribution for one or more random variables and looks at different methods to derive the distribution of a function of random variables. These techniques are then used to prove some of the results underpinning hypothesis test and confidence interval calculations, such as for the t-test or the F-test. With these tools to hand, the module moves on to look at how to fit models (probability distributions) to sets of data. A standard technique, known as the method of maximum likelihood, is introduced, which is then used to fit the model to the data to obtain point estimates of the model parameters and to construct hypothesis tests and confidence intervals for these parameters. The module concludes with a directed reading task to explore some of the ideas of Bayesian inference. Outline Syllabus includes: Joint, marginal and conditional distributions of discrete and continuous random variables; Generating functions; Transformations of random variables; Sampling distributions; Point and interval estimation; Properties of estimators; Maximum likelihood; Hypothesis testing; Neyman-Pearson lemma; Maximum likelihood ratio test. Bayesian inference: prior and posterior distributions, conjugate prior, loss function, Bayesian estimators and credible intervals.

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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 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 for further details.

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Analysis of variance is a fundamentally important method for the statistical analysis of data. It is used widely in biological, medical, psychological, sociological and industrial research when we wish to compare more than two treatments at once. In analysing experimental data, the appropriate form of analysis of variance is determined by the design of the experiment, and we shall therefore discuss some aspects of experimental design in this module. Lectures are supplemented by computing classes which explore the analysis of variance facilities of the statistical package R. Syllabus: One-way ANOVA (fixed effects model); alternative models; least squares estimation; expectations of mean squares; distributional results; ANOVA table; follow-up analysis; multiple comparisons; least significant difference; confidence intervals; contrasts; orthogonal polynomials; checking assumptions; residual plots; Bartlett's test; transformations; one-way ANOVA (random effects model); types of experiment; experimental and observational units; treatment structure; randomisation; replication; blocking; the size of an experiment; two-way ANOVA; the randomised complete block design; two-way layout with interaction; the general linear model; matrix formulation; models of full rank; constraints; motivations for using least squares; properties of estimators; model partitions; extra sum of squares principle; orthogonality; multiple regression; polynomial regression; comparison of regression lines; analysis of covariance; balanced incomplete block designs; Latin square designs; Youden rectangles; factorial experiments; main effects and interactions.

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This module considers statistical analysis when we observe multiple characteristics on an experimental unit. For example, a sample of students' marks on several exams or the genders, ages and blood pressures of a group of patients. We are particularly interested in understanding the relationships between the characteristics and differences between experimental units. Outline syllabus includes: measure of dependence, principal component analysis, factor analysis, canonical correlation analysis, hypothesis testing, discriminant analysis, clustering, scaling.

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In this module you will develop the advanced English language skills needed for post graduate studies in Science. This includes the ability to interpret and evaluate authentic scientific texts; analyse, discuss, summarise and synthesise written and visual information both in writing and orally; organise written texts effectively and submit them in grammatically accurate English, and present the results of research orally in a coherent and stimulating way.

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This module will focus on basic features of stochastic processes and time series analysis. It includes: Markov chains on discrete state spaces, communication classes, transience and recurrence, positive recurrence, stationary distributions. Markov processes on discrete state spaces, exponential distribution, embedded Markov chain, transition graphs, infinitesimal generator, transition probabilities, stationary distributions, skip-free Markov processes. Stationary time series: Stationarity, autocovariance and autocorrelation functions, partial autocorrelation functions, ARMA processes. ARIMA Model Building and Testing: Estimation, Box Jenkins, criteria for choosing between models, diagnostic tests for the residuals of a time series after estimation. Forecasting: Holt-Winters, Box-Jenkins, prediction bounds.

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This module considers the development and application of stochastic models in two specific areas. The ecological part is focused on the analysis of data collected on wild animals. Particular attention will be given to estimating how long wild animals live, and also to estimating the sizes of mobile animal populations. The medical part also considers the estimation of survival, but in this case for human beings, with less data loss due to individuals leaving the study than is typical in ecological studies. In survival data it is often known only that individuals survived for a certain period of time, with exact survival time being unknown. This is called censoring and its implications will be discussed in detail. Outline Syllabus includes: Estimating abundance; estimating survival; using covariates; multi-state models; parameter redundancy; human survival data with censoring; the hazard and related functions; parametric and semiparametric survival models.

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This module considers statistical analysis when we observe multiple characteristics on an experimental unit. For example, a sample of students' marks on several exams or the genders, ages and blood pressures of a group of patients. We are particularly interested in understanding the relationships between the characteristics and differences between experimental units. Regression methods can be used if one characteristic can be treated as a response variable and the others as explanatory variables. Variable selection on the explanatory variables can be daunting if the number of characteristics is large and suitable methods will be investigated. Outline Syllabus includes: measure of dependence, principal component analysis, factor analysis, canonical correlation analysis, hypothesis testing, discriminant analysis, clustering, scaling, information criterion methods for variable selection, false discovery rate, penalised maximum likelihood.

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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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This applied statistics module focusses on problems that occur in the fields of ecology, biology, genetics and psychology. Motivated by real examples, you will learn how to define and fit stochastic models to the data. In more complex situations this will mean using optimisation routines in MATLAB to obtain maximum likelihood estimates for the parameters. You will also learn how construct, fit and evaluate such stochastic models. Outline Syllabus includes: Function optimisation. Basic likelihood tools. Fundamental features of modelling.  Model selection. The EM algorithm. Simulation techniques. Generalised linear models.

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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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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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This module will focus on sample surveys, experimental design and clinical trials. It will consider the key principles for designing a survey or an experiment to ensure that any inferences drawn about the population being studied or about the treatments being compared are valid. The discussion of experimental design will be extended into the field of clinical trials (trials conducted on humans) with the added considerations that this introduces. Use will be made of R and Excel for practical examples. Outline Syllabus includes: simple, stratified, cluster and multi-stage sampling; ratio and regression estimators; questionnaire design; completely randomised, randomised block and Latin square designs; factorial designs, fractional replication and confounding; incomplete block designs; analysis of covariance; practical aspects of clinical trials; parallel group trials, sample size; multicentre and crossover trials.

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Teaching and Assessment

The programme is assessed by coursework involving: complex theoretical questions, analysis of real-world data using appropriate computing packagse over a range of areas of application; written unseen 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 the 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.


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. 

Meet our staff in your country

For more advise about applying to Kent, you can meet our staff at a range of international events.

English language entry requirements

For detailed information see our English language requirements web pages. 

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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Dr Rachel McCrea: Research Associate

Integrated population modelling of dependent data structures.

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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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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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The 2017/18 annual tuition fees for this programme are:

International Masters in Statistics - MSc at Canterbury:
UK/EU Overseas
Full-time N/A £14670

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.*

The University will assess your fee status as part of the application process. If you are uncertain about your fee status you may wish to seek advice from UKCISA before applying.

General additional costs

Find out more about accommodation and living costs, plus general additional costs that you may pay when studying at Kent.


Scholarships and funding information

Related to this course