Full time 9 Month(s), Part time 24 Month(s)
This course has a strong theoretical and methodological component to supplement a focus on applications of statistics to real life scientific problems. You can opt to follow pathways in medical, pharmaceutical or environmental statistics, depending on your field of interest. Graduates tend to enter careers as practising statisticians, university research assistants or go on to study for a PhD.
For each pathway you will follow a set of compulsory modules covering core theory and methods, applied statistical modelling and practical skills in topics such as statistical computing, scientific writing, presentation and consultancy. You will also study optional modules tailored to your research interests and career aspirations.
You will study a range of modules as part of your course, some examples of which are listed below.
This module equips students with a range of skills necessary for applied statistical work. Students will develop a working knowledge in four major areas: computing, scientific writing, oral presentation and statistics in context.
By completing this module, students will demonstrate an understanding of the linux operating system, R software, and LaTeX. Additionally, they will gain an understanding of statistical tabulation, public speaking and will receive a series of guest lectures which will focus on substantive problem-areas in medicine, finance, the environment, public health and statistical consulting.
This module presents the key tools for statistical inference, stressing the fundamental role of the likelihood function. It addresses how the likelihood function, that is, the probability of the observed data viewed as a function of unknown parameters, can be used to make inference about those parameters, in addition to working with models which do not assume the data are independent and identically distributed. Students will also be introduced to basic computational aspects of likelihood inference that are required in many practical applications.
Students will engage with a range of features, including the definition of the likelihood model for multi-parameter models, and how it is used to calculate point estimates, the asymptotic distribution of the maximum likelihood estimator, the definition and use of orthantology, and the simple use for computational methods to calculate maximum likelihood estimates.
On completion of this module, students will be able to appreciate how information about the unknown parameters is obtained and summarised via the likelihood function, in addition to the level of skill required to calculate the likelihood function for some statistical models which do not assume independently identically distributed data, as well as a developed understanding of the inter-relationships between parameters, and the concept of orthogonality.
Generalised linear models are now one of the most frequently used statistical tools of the applied statistician. They extend the ideas of regression analysis to a wider class of problems such as the relationship between a response and one or more explanatory variables. This module discusses applications of the generalised linear models to a diverse range of practical problems involving data from the area of biology, social sciences and time series to name a few, and aims to explore the theoretical basis of these models. The syllabus consists of formulating sensible models for a relationship between a response and one or more explanatory variables, taking account of the motivation for data collection, whilst checking these models in the statistical package R, producing confidence intervals and tests corresponding to questions of interest, and stating conclusions in everyday language.
On successful completion of this module, students will develop the ability to apply their knowledge of model formulation in order to judge how the probability of success will depend on the patient’s age, weight, blood pressure and so on. Finally, students will become familiar with a common algorithm called ‘iteratively reweighted last squares’ algorithm, which is intended for the attention of parameters.
Introducing the Bayesian view of statistics, this module stresses its philosophical contrasts with classical statistics, its facility for including information other than the data into the analysis, and its current approach toward inference and model selection. Students will learn how to identify and interpret the conjugate prior, and will develop the ability to calculate and interpret the posterior distribution, the posterior predictive distribution and also the Bayes rule and risk for a variety of loss functions, in addition to achieving the level of skill required to derive, calculate and interpret the marginal likelihood.
Further skills provided on completion of this module include the ability to differentiate situations where a subjective and an objective Bayesian approach are appropriate, as well as when importance sampling is necessary, and whether to derive its properties and to implement it efficiently in R. Students will also gain transferrable knowledge in recognising where different approaches in statistical inference are used in real situations and interpret the results appropriately.
This module introduces the expectation-maximisation algorithm, an iterative algorithm for obtaining the maximum likelihood estimate of parameters in problems with intractable likelihoods. Students will explore the use of Markov chain Monte Carlo (MCMC) methods, and will discover the features of the Metro-Hastings algorithm, with emphasis on the Gibbs sampler, independence sampler and random walk Metropolis. Whilst relating to this, students will consider how such methods are closely integrated with Bayesian modelling techniques such as hierarchal modelling, random effects and mixture modelling.
Data augmentation will receive recurring coverage over the course of the module. Students will also gain transferrable knowledge of the usefulness of computers in assisting statistical analysis of complex methods, in addition to experience with the computer statistical package R.
This module aims to develop the asymptotic theory, and associated techniques for modelling and inference, associated with the analysis of extreme values of random processes. The module focuses on the mathematic basis of the models, the statistical principles for implementation and the computational aspects of data modelling.
Students will develop an appreciation of, and facility in, the various asymptotic arguments and models, and will also gain the ability to fit appropriate models to data using specially developed R software, in addition to a working understanding of fitted models. Knowledge in R software computing is an essential skill that is transferrable with a wide range of modules on the mathematics programme, and beyond.
Clinical trials are planned experiments on human beings designed to assess the relative benefits of one or more forms of treatment. For instance, we might be interested in studying whether aspirin reduces the incidence of pregnancy-induced hypertension, or we may wish to assess whether a new immunosuppressive drug improves the survival rate of transplant recipients.
This module combines the study of technical methodology with discussion of more general research issues, beginning with a discussion of the relative advantages and disadvantages of different types of medical studies. The module will provide a definition and estimation of treatment effects. Furthermore, cross-over trials, issues of sample size determination, and equivalence trials are covered. There is an introduction to flexible trial designs that allow a sample size re-estimation during the ongoing trial. Finally, other relevant topics such as meta-analysis and accommodating confounding at the design stage are briefly discussed.
Students will gain knowledge of the basic elements of clinical trials. They will develop the ability to recognise and use principles of good study design, and will also be able to analyse and interpret study results to make correct scientific inferences.
This module discusses several genomics technologies by first of all putting them into their biological context and secondly describing types of biological questions that can be answered with the data from these technologies, with the aim of gaining knowledge and expertise necessary to identify the appropriate analysis methods to use when answering biological questions using genomic data. Technologies that are discussed are DNA sequencing, SNP, microarrays and blotting, in addition to other proteomics methods. Students will also learn how they can analyse genomic data and interpret their findings in text.
On completion of this module and in addition to the outcomes above, students will develop the ability to discuss the question of interest and the statistical findings with a non-statistician.
Introducing epidemiology, the study of the distribution and determents of disease in human population, this module presents its main principles and statistical methods. The module addresses the fundamental measures of disease, such as indicence, prevalence, risk and rates, including indices of morbidity and mortality.
Students will also develop awareness in epidemiologic study design, such as ecological studies, surveys, and cohort and case-control studies, in addition to diagnostic test studies. Epidemiological concepts will be addressed, such as bias and confounding, matching and stratification, and the module will also address calculation of rates, standardisation and adjustment, as well as issues in screening.
This module provides students with a historical and general overview of epidemiology and related strategies for study design, and should enable students to conduct appropriate methods of analysis for rates and risk of disease. Students will develop skills in critical appraisal of the literature and, in completing this module, will have developed an appreciation for epidemiology and an ability to describe the key statistical issues in the design of ecological studies, surveys, case-control studies, cohort studies and RCT, whilst recognising their advantages and disadvantages.
This module presents an approach to the analysis of longitudinal data, based on statistical modelling and likelihood methods of parameter estimation and hypothesis testing. Among other topics, students will learn about the exploratory and simple analysis strategies, the independence working assumption, normal linear model with correlated errors and generalised estimation questions.
Students will develop an understanding in dealing with correlated data commonly arising in longitudinal studies, as well as an awareness of issues associated with collecting and analysing longitudinal data, whilst gaining a higher level of knowledge different modelling assumptions used in the analysis and their relations to the scientific aims of the study.
On module completion, students will gain the ability to explain the difference between longitudinal studies and cross-sectional studies, in addition to the knowledge required to select appropriate techniques to explore data, and the ability to compare different approaches to estimation and their usage in the analysis. Finally, students will obtain the skill level required to build statistical models for longitudinal data and draw valid conclusions from their models.
This module explores the relationship between physiology and its representation through mathematic models. Students will gain knowledge of how the parameters of such models may be estimated form data, and will develop an understanding of the design of close-escalation and interplay between concerns of scientific enquiry and the safety of human subjects.
Students will also gain a range of transferrable skills that will reinforce knowledge in areas covered in other modules on the programme, including the ability to express scientific problems in a mathematical language, an enlightened understanding of Bayesian decision procedures, non-linear models and non-linear mixed models, in addition to general computing skills and its use in statistical modelling and analysis.
On module completion, students will be able to explain how certain mathematic models used to describe the uptake and distribution of drugs administered to the body can be served from physiological considerations. Students will also gain the necessary experience to derive estimates of model parameters from appropriate data, and the ability to develop and evaluate designs from close-escalation studies.
This module addresses a range of topics relating to survival data; censoring, hazard functions, Kaplan-Meier plots, parametric models and likelihood construction will be discussed in detail. Students will engage with the Cox proportional hazard model, partial likelihood, Nelson-Aalen estimation and survival time prediction and will also focus on counting processes, diagnostic methods, and frailty models and effects.
The module provides an understanding of the unique features and statistical challenges surrounding the analysis of survival avant history data, in addition to an understanding of how non-parametric methods can aid in the identification of modelling strategies for time-to-event data, and recognition of the range and scope of survival techniques that can be implemented within standard statistical software.
General skills will be developed, including the ability to express scientific problems in a mathematical language, improvement of scientific writing skills, and an enhanced range of computing skills related to the manipulation on analysis of data.
On successful completion of this module, students will be able to apply a range of appropriate statistical techniques to survival and event history data using statistical software, to accurately interpret the output of statistical analyses using survival models, fitted using standard software, and the ability to construct and manipulate likelihood functions from parametric models for censored data. Students will also gain observation skills, such as the ability to identify when particular models are appropriate, through the application of diagnostic checks and model building strategies.
This module introduces students to the kinds of statistical methods commonly used by epidemiologists and statisticians to investigate the relationship between risks of disease with environment factors. Students will discover motivation examples for methods in course, and will engage with spatial point-processes, including the theory and methods for the analysis of point-processes in two-dimensional space.
A number of published studies will be used to illustrate the methods described, and students will learn how to perform similar analyses using the statistical package, R. Students will learn methods and theory for analysing point-patterns, such as univariate and bivariate K-functions, methods for analysing care control data, including kernel intensity estimation, binary regression and generalised additive models. Students will also explore spatial generalised linear-mixed models including Poisson models for counts of a disease in regions and the concept of ecological bias, along with modelling elevated disease risk due to the presence of a point source and continuous spatial variation including the Gaussian geostatistical model, variograms and spatial prediction.
Students will develop the ability to recognise the difference between point process data, area-level data and geostatistical data, and the skills required to define and estimate the intensity of K functions for a spatial point process. Finally, successful students will be able to perform basic analyses of case-control and geostatistical data, along with a broad understanding of practical issues involved in undertaking environmental epidemiology studies.
Information contained on the website with respect to modules is correct at the time of publication, but changes may be necessary, for example as a result of student feedback, Professional Statutory and Regulatory Bodies' (PSRB) requirements, staff changes, and new research.
Director of Studies: Dr Deborah Costain.
Duration: nine months full-time.
Entry requirements: Second class honours degree, or its equivalent, in a subject with a strong Mathematics or Statistics component. Conversion modules are available.
IELTS: 6.5 or equivalent.
Assessment: Coursework, examination and dissertation.
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