Statistics MSc

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.

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.

This module is concerned with 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 extends the theoretical aspects of statistical inference by developing the theory of the generalised linear model and its practical implementation. Initially, designing of experiments in order to explore relationship between factors and a response is viewed within the context of Linear models.

The module then extends the understanding and application of statistical methodology established in previous courses to the analysis of discrete data and survival, which frequently occur in diverse applications. You will be trained in the use of an appropriate high-level statistical package.

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.

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 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.

The aim of this module is to explore the application of probability and statistics to a variety of practical, open-ended problems. You will study specific projects through workshops and student-led group activities enabling you to develop skills in model development and refinement, report writing and teamwork.

Group project one 

• Development of group/communication skills
• Report in the form of a poster and brief presentation

Group project two 

• Development of modelling methodology and problem-solving
• Formal report and oral presentation

Group project three

• To display originality in the applications of statistical approaches to a substantial unseen and open-ended problem
• Supported by weekly group meetings

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.