The MSc Statistics and Applied Probability is intended for students with a degree in mathematics (or a related subject with a substantial mathematical content). Some knowledge of probability and statistics would be helpful to start the course.
The course is designed such that the module 'Fundamentals of Statistics' is either a pre or a co-requisite for all other modules offered in the course. You will study for 180 credits, split across 120 credits worth of taught modules and a 60-credit research project.
Fundamentals of Statistics
In this module you will explore the fundamental principles and techniques underlying modern statistical modelling and data analysis. The course will cover a 'common core' consisting of statistical concepts and methods, linear models, probability techniques and Markov chains. You will gain experience of using a statistical package and interpreting its output.
In addition, you will study more advanced material concerned with the two main theories of statistical inference, namely classical (frequentist) inference and Bayesian inference. Topics such as sufficiency and best-unbiased estimators are explored in detail. There is special emphasis on the exponential family of distributions. Topics in Bayesian inference include basic ingredients (prior, likelihood and posterior), conjugacy, vague peior knowledge, marginal and predictive inference, decision theory, normal inverse gamma inference, and categorical data.
In this module the ideas of discrete-time Markov chains are extended to include more general discrete-state space stochastic processes evolving in continuous time and applied to a range of stochastic models for situations occurring in the natural sciences and industry. You will be introduced to Poisson processes and birth-and-death processes. This is followed by more extensive studies of epidemic models and queueing models, and introductions to component and system reliability.
You will work on a substantial investigation on a topic in statistics or probability. The study will be largely self-directed, although a supervisor will provide oversight and input where necessary. The topic could be based on the statistical analysis of a substantial dataset, an investigation into the statistical methodology or an investigation into a topic of applied probability or probability theory. It is expected that most projects will contain an element of statistical computing.
You must choose three modules, but you are not able to take both Uncertainty Quantification and Statistical Machine Learning.
Advanced Stochastic Processes
This module considers three advanced topics in stochastic process theory: martingales, Brownian motion and renewal processes. The main properties of and theorems for martingales are developed along with the basic properties of Brownian motion which you will investigate and methods for calculating probabilities and expectations associated with Brownian motion are described. The aim of the module is to gain experience of a range of stochastic models and techniques for their analysis.
Applied Multivariate Statistics
During this module you will explore the analysis of multivariate data, in which the response is a vector of random variables rather than a single random variable. A theme running through the module is that of dimension reduction. Key topics to be covered include: principal components analysis, whose purpose is to identify the main modes of variation in a multivariate dataset; modelling and inference for multivariate data, including multivariate regression data, based on the multivariate normal distribution; classification of observation vectors into subpopulations using a training sample; canonical correlation analysis, whose purpose is to identify dependencies between two or more sets of random variables. Further topics to be covered include methods of clustering and multidimensional scaling.
This module explores how computers allow the easy implementation of standard, but computationally intensive, statistical methods and also explores their use in the solution of non-standard analytically intractable problems by innovative numerical methods. Particular topics covered include a selection from simulation methods, Markov chain Monte Carlo methods, the bootstrap and nonparametric statistics, statistical image analysis, and wavelets. You will gain experience of using a statistical package and interpreting its output.
Statistical Machine Learning
This module is a topic at the interface between statistics and computer science, concerning models that can adapt to and make predictions based on data. This module builds on the principles of statistical inference and linear regression to introduce a variety of methods of clustering, dimension reduction, regression and classification.
Much of the focus is on the bias-variance trade-off and on methods to measure and compensate for overfitting. The learning approach is hands-on; you will be using R extensively in studying contemporary statistical machine learning methods, and in applying them to tackle challenging real-world applications.
Stochastic Financial Modelling
The aim of the module is to provide an introduction to probabilistic and stochastic modelling for investment strategies, and for the pricing of financial derivatives in risky markets. The probabilistic ideas that underlie the problems of portfolio selection, and of pricing and hedging options, are introduced. You will gain experience of a topic of considerable contemporary importance, both in research and in applications. You will undertake a project which will involve independent reading, and a written report.
Time Series and Forecasting
This module will provide a general introduction to the analysis of data that arise sequentially in time. Several commonly occurring models will be discussed and their properties derived. Methods for model identification for real-time series data will be considered. Techniques for estimating the parameters of a model, assessing its fit and forecasting future values will be developed. You will gain experience of using a statistical package and interpreting its output.
This module aims to provide a comprehensive introduction to the key concepts in the field of uncertainty quantification. You will be introduced to a variety of techniques which are useful in UQ and will focus on a more in-depth study of selected application areas. The module will cover:
- sensitivity analysis
- Bayesian approaches to inverse problems
- spectral decomposition methods
- data assimilation and filtering
- interpolation and approximation using orthogonal polynomials
The above is a sample of the typical modules that we offer but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. This course page may be updated over the duration of the course, as modules may change due to developments in the curriculum or in the research interests of staff.
Teaching methods and assessment
Modules are mainly delivered through lectures and workshops and/or problem classes for smaller groups.
You will typically be assessed by an examination or coursework at the end of the semester in which a given module is taught.
The MSc offers you the opportunity to further your knowledge in both statistics and applied probability, which will be beneficial for a professional career in statistics or as a solid basis for research in statistics or applied probability.
Average starting salary and career progression
100% of postgraduates in the School of Mathematical Sciences secured work or further study within six months of graduation. The average starting salary was £30,800, with the highest being £60,000.*
* Known destinations of full-time home postgraduates who were available for employment, 2016/17. Salaries are calculated based on the median of those in full-time paid employment within the UK.
Careers support and advice
We offer individual careers support for all postgraduate students whatever your course, mode of study or future career plans.
You can access our Careers and Employability Service during your studies and after you graduate. Expert staff will help you research career options and job vacancies, build your CV or résumé, develop your interview skills and meet employers.
More than 1,500 employers advertise graduate jobs and internships through our online vacancy service. We host regular careers fairs, including specialist fairs for different sectors.
As a student on this course, we do not anticipate any extra significant costs, alongside your tuition fees and living expenses. You should be able to access most of the books you’ll need through our libraries, though you may wish to purchase your own copies which you would need to factor into your budget.
Scholarships and bursaries
School scholarships for UoN UK alumni
For 2020/21 entry, 10% Alumni scholarships may be offered to former University of Nottingham graduates who have studied at the UK campus.
Government loans for masters courses
Masters student loans of up to £10,906 are available for taught and research masters courses. Applicants must ordinarily live in the UK or EU.
International and EU students
Masters scholarships are available for international and EU students from a wide variety of countries and areas of study. You must already have an offer to study at Nottingham to apply. Please note closing dates to ensure you apply for your course with enough time.
We provide guidance on funding your degree, living costs and working while you study. You can also access specific funding opportunities, entry requirements and other resources for students from specific countries.