Statistics PGDip

Program Overview

This postgraduate diploma is designed for individuals seeking advanced training in statistics. The program combines theoretical knowledge with practical skills, blending classical and modern methods with real-world applications. Students develop skills in statistical modeling, data analysis, and project management, preparing them for careers as statisticians, data scientists, or in other roles requiring advanced statistical expertise.

Program Outline

Degree Overview:

Our PGDip in Statistics follows the same taught course structure as our Royal Statistical Society (RSS) accredited master's programme, but without the dissertation component that comprises the final part of the master's year. As with the master's programme, the PGDip combines a blend of theoretical study with real-world application. You will develop advanced statistical skills and knowledge, while having the opportunity to put what you learn into practice and gain valuable, real-world experience. In addition to acquiring advanced technical knowledge, you will also develop project management and communication skills. A carefully structured approach will enable you to develop and strengthen your essential core skills in both classical and modern statistical methods and inference before progressing to the more advanced and specialist modules. The specialist modules cover a diverse range of statistical topics reflecting both areas of Departmental research expertise and the requirements of leading employers of statisticians. You will be supported in selecting those specialist modules that best reflect your own interests and career aspirations. Alongside the technical modules, you will undertake a module to advance key transferable skills in programming and communications. Programming, and the confident use of statistical software, enables the analysis of large and complex data sets, whilst communication is an essential skill for all statisticians, who must be able to engage in dialogue with members of the project team, stakeholders and end-users. You will be based in the Department of Mathematics and Statistics, where you will have access to specialist software and equipment. You will have the opportunity to engage with academic staff members, all of whom are active statistical researchers, and to participate in departmental research colloquia and seminars should you choose to do so.

Outline:

Core Modules:

• Statistical Fundamentals I: This module will only be completed by students who, depending on their mathematical background, require an introduction, at graduate level, to two core areas which are essential building blocks to further advanced study of statistical modelling, methodology and theory.
Students will study either this module or the other core module titled ‘Statistical Foundations I' but not both.
• The areas that will be covered are statistical inference using maximum likelihood and generalised linear models (GLMs).
Following on from this, GLMs, a widely and routinely used family of statistical models, will be introduced as an extension of the linear regression model.
• Statistical Fundamentals II: This module will develop the core topic of maximum likelihood inference previously introduced in MATH501 Statistical Fundamentals I by expanding on numerical and theoretical aspects.
Numerical aspects will include obtaining the maximum likelihood estimate using numerical optimisation functions in R, and using the profile likelihood function to obtain both the maximum likelihood estimate and confidence intervals. Theoretical elements covered will include derivation of asymptotic distributions for the maximum likelihood estimator, deviance and profile deviance.
• The second half of the module will introduce Bayesian inference as an alternative to maximum likelihood inference.
Building on existing knowledge of the likelihood function, the prior and posterior distributions will be introduced. For simple models, analytical forms for the posterior distribution will be introduced and point estimates for the parameter obtained. For more complex models, numerical methods of sampling from the posterior distribution will be demonstrated.
• Statistical Learning: This module provides an introduction to statistical learning.
General topics covered include big data, missing data, biased samples and recency. Likelihood and cross-validation will be introduced as generic methods to fit and select statistical learning models. Cross-validation will require an understanding of sample splitting into calibration, training and validation samples. The focus will then move to handling regression problems for large data sets via variable reduction methods such as the Lasso and Elastic Net. A variety of classification methods will be covered including logistic and multinomial logistic models, regression trees, random forests and bagging and boosting. Examination of classification methods will culminate in neural networks which will be presented as generalised linear modelling extensions. Unsupervised learning for big data is then covered including K-means, PAM and CLARA, followed by mixture models and latent class analysis.
• Statistics in Practice: The aim of this module is to provide students with a range of skills that are necessary for applied statistical work including team-working, oral presentation, statistical computing, and the preparation of written reports including statistical analyses.
All students will obtain a thorough grasp of R (including R objects and functions, graphs, basic simulations and programming) and be given an introduction to a second statistical computing package.
• Students will also learn how to utilise LaTex for writing a complex and structured scientific report that may include mathematical formulae, tables and figures, as well as learn the intricacies of effective scientific writing style such as grammar, referencing, and the presentation of results in appropriate tables and graphs.
They will enhance their oral presentation technique using LaTex Beamer to create slides that include complex mathematical formulae, as well as embark on an in-depth team project using Git, R Markdown or iPython notebooks.

Optional Modules:

• Clinical Trials: 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.
• Computationally Intensive Methods: 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.
• Extreme Value Theory: Extreme Value Theory is an area of probability theory which describes the stochastic behaviour of events occurring in the tail of a distribution (eg.
block maxima). This course will cover both an overview of key theoretical results and the statistical modelling approaches which are motivated by these results. Theoretical results covered will include limiting distributions for block maxima and Peaks Over Threshold events in the case of both independent and time-series data. Modelling will involve the development of extreme value statistical models and their application to data sets taken from financial and environmental applications. The concept of extremal dependence will be introduced. For example, participants in a survey or clinical trial may drop-out of the study, measurement instruments may fail, or human error invalidate instrumental readings. In this module you will learn about the different ways in which missing data can arise, and how these can be handled to mitigate the impact of the missingness on the data analysis. Topics covered include single imputation methods, Bayesian imputation, multiple imputation (Rubin's rules, chained equations and multivariate methods, as well as suitable diagnostics) and modelling dropout in longitudinal modelling.
• Modelling Multilevel and Longitudinal Data: Hierarchical data arise in a multitude of settings, specifically whenever a sample is grouped (or clustered) according to one or more factors with each factor having many levels.
For instance, school pupils may be grouped by teacher, school and local education authority. There is a hierarchical structure to this grouping since schools are grouped within local education authority and teachers are grouped within schools. If multiple measurements of a response variable, say test score, are made for each pupil across multiple measurement times, the data are also longitudinal. The differences between marginal and conditional models, and the advantages and disadvantages of each, will be discussed. Longitudinal data will be introduced as a special case of hierarchical data motivating the need for temporal dependence structures to be incorporated within LMMs. Finally, the drawbacks of LMMs will be used to motivate generalised linear mixed effects models (GLMMs), with the former a special case of the latter. GLMMs broaden the scope of data sets which can be analysed using mixed-effects models to incorporate all common types of response variable.
• All modelling will be carried out using the statistical software package R.
• Principles of Epidemiology: 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 incidence, 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.
• Survival and Event History Analysis: 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.
• 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.
• Time Series Analysis: The course is designed to provide foundational knowledge in linear and non-linear time-series analysis through building awareness of various well used time-series models.
While the module focuses on univariate analysis, students will have time to read around lecture notes and materials to extend their understanding of these methods. By the end of the course, the student should understand both the theoretical and practical foundations of time-series analysis, how to fit, and choose from a range of models. They will understand different methods of evaluating time-series model performance and how these models can be used to provide forecasts.

Assessment:

Teaching in our department is delivered through a range of methods to create the best possible learning experience. Alongside traditional lectures, you can expect to benefit from small workshop groups, which are guided by tutors who are active researchers and offer you an opportunity to put what you have learnt in lectures into practice. We also run computer lab sessions focused on developing your programming and analytical skills through the use of specialist statistical software. We utilise a range of assessment methods that are designed to support and encourage you to demonstrate your knowledge and ability fully. The majority of our modules include end of year exams, and you will also undertake research projects, group work and presentations.

Teaching:

We utilise a range of teaching methods, including lectures, workshops, seminars, and practical sessions, to provide a well-rounded and interactive learning experience. These methods are tailored to enhance understanding and promote engagement. You will be taught by expert staff who are all active researchers in the field of statistics.

Careers:

Statistics graduates are highly employable, having in-depth specialist knowledge and a wealth of skills. Through this degree, you will graduate with a comprehensive skill set, including data analysis and manipulation, logical thinking, problem-solving and quantitative reasoning, as well as advanced knowledge of the discipline. Statistics plays a valuable role in all businesses and enterprises. As a result, a range of industries, including education, finance, forensics, health, market research, and transport, actively seek statisticians for crucial roles. The starting salary for many graduate statistical roles is highly competitive, and popular career options include:

• Assistant Statistician
• Data Analyst
• Market Researcher
• Data Scientist
• Statistical Officer
• Teacher

Other:

You will have access to specialist software and equipment within the Department of Mathematics and Statistics. You will also have the opportunity to engage with academic staff members, all of whom are active statistical researchers, and to participate in departmental research colloquia and seminars should you choose to do so. The University reserves the right to make changes to advertised courses. In exceptional circumstances that are beyond the University’s reasonable control (Force Majeure Events), we may need to amend the programmes and provision advertised. In this event, the University will take reasonable steps to minimise the disruption to your studies. If a course is withdrawn or if there are any fundamental changes to your course, we will give you reasonable notice and you will be entitled to request that you are considered for an alternative course or withdraw your application.

Fees and Funding

Location Full Time (per year) Part Time (per year) Home £9,065 £4,530 International £19,430 £9,715

Additional costs

There may be extra costs related to your course for items such as books, stationery, printing, photocopying, binding and general subsistence on trips and visits. Following graduation, you may need to pay a subscription to a professional body for some chosen careers. Specific additional costs for studying at Lancaster are listed below.

College fees

Lancaster is proud to be one of only a handful of UK universities to have a collegiate system. Every student belongs to a college, and all students pay a small College Membership Fee which supports the running of college events and activities. Students on some distance-learning courses are not liable to pay a college fee. For students starting in 2023 and 2024, the fee is £40 for undergraduates and research students and £15 for students on one-year courses. Fees for students starting in 2025 have not yet been set.

Computer equipment and internet access

To support your studies, you will also require access to a computer, along with reliable internet access. You will be able to access a range of software and services from a Windows, Mac, Chromebook or Linux device. For certain degree programmes, you may need a specific device, or we may provide you with a laptop and appropriate software - details of which will be available on relevant programme pages. A dedicated IT support helpdesk is available in the event of any problems. The University provides limited financial support to assist students who do not have the required IT equipment or broadband support in place.

Application fees and tuition fee deposits

For most taught postgraduate applications there is a non-refundable application fee of £40. We will let you know in your offer letter if a deposit is required and you will be given a deadline date when this is due to be paid.