Statistics MSc

In this module, the fundamental principles and techniques underlying modern statistical and data analysis will be introduced. You will gain experience in using a statistical package and interpreting its output. The course will cover a 'common core' consisting of:

• statistical concepts and methods
• linear models
• probability techniques
• Markov chains

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 will look at developing the concepts of frequentist and classical statistical inference. You will also learn to consider parameter estimation and the properties of parameters from both a mathematical and computational perspective.

Topics covered include maximum likelihood estimation, confidence intervals and likelihood ratio tests. There is an emphasis on the exponential family of distributions, which includes many standard distributions such as the normal, Poisson, binomial and gamma.

You will also explore the role of computers in performing statistical inference for non-standard (i.e. analytically intractable) problems. You’ll be introduced to optimisation methods, the bootstrap algorithm and simulation techniques including Monte Carlo methods in relation to problems of statistical inference.

Modelling is a fundamental part of statistics, enabling us to analyse and interpret data to understand the world and make predictions.

This module studies extensions of statistical modelling beyond the linear model, including non-linear and non-parametric regression and generalised linear models (GLMs) for binary and count data. These topics are the foundations of statistical machine learning.

You will gain an understanding of the theoretical foundations of these areas along with the knowledge of how to implement the techniques in a computationally efficient manner to analyse data.

This module complements the frequentist statistical approach studied in the Advanced Statistical Inference module.

Bayesian inference has established itself as a popular alternative to traditional frequentist methods – and some of its techniques and ideas have found their way into many modern machine learning algorithms.

You will be introduced to the core concepts of the prior and posterior distributions of the parameters that underpin Bayesian statistics, covering the fundamental topics of prior elicitation, model conjugacy, predictive inference and model choice.

You will also study Markov Chain Monte Carlo (MCMC) and its implementation using statistical software, exploring a range of challenging modelling scenarios such as state-space models, dynamic linear models, mixed models and hierarchical models.

This module will help broaden your knowledge of statistics by introducing important contemporary topics in multivariate analysis. The focus is on application and high-level understanding, as well as light coverage of the underpinning mathematics behind each method.

You will cover key topics including:

• vector and matrix algebra ideas relevant to multivariate statistics, including the eigen and singular value decompositions

• methods for dimension reduction including principal components analysis, canonical correlation analysis and factor analysis

• multivariate regression methods

• classification methods, such as linear discriminant analysis

• multivariate normal distributions and their use in multivariate analysis of variance tests

• exploratory data analysis methods such as clustering tools, and multi-dimensional scaling, as well as other data visualisation techniques

• statistical software for conducting analysis of multivariate data

This module will cover several commonly occurring time series (temporal) models and their derived properties. You will learn methods for model identification for real-time series data and you’ll develop techniques for estimating the parameters of a model, assessing its fit and forecasting future values.

You will also learn methodology for spatial data, such as random fields and point processes, as well as inference for spatial data and interpolation for estimation. Throughout the module, computational methods will play an important role in implementing the methods of inference and prediction.

This module covers topics at the intersection between statistics and computer science, such as models that can adapt to and make predictions based on data.

It builds on the principles of statistical inference and linear regression to introduce neural networks as an advanced regression and classification tool. You will learn about bias-variance trade-off and methods to measure and compensate for overfitting, and their applications to AI.

The hands-on learning method using computing to study neural networks will help you apply them in tackling real-world challenges.

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.

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.