Statistical Science (Distance Learning) MSc

In this course the fundamental principles and techniques underlying modern statistical and data analysis will be introduced. The course will cover the core foundations of statistical theory consisting of:

• probability distributions and techniques;
• statistical concepts and methods;
• linear models

The course highlights the importance of computers, and in particular, statistical packages, in performing modern statistical analysis. You will be introduced to the statistical package R as a statistical and programming tool and will gain hands-on experience in interpreting and communicating its output.

This module is concerned with frequentist (classical/frequentist) statistical inference, both its theory and its applications and builds on the fundamental ideas of statistics introduced in the module “Foundations of Statistics”.

The following topics are explored and the Delta Method is also presented:

• maximum likelihood estimation
• properties of estimators
• confidence intervals
• likelihood ratio tests

There is emphasis on the exponential family of distributions, which includes many standard distributions such as the normal, Poisson, binomial and gamma. You will also explore how computers can be utilised to perform statistical inference for non-standard (i.e. analytically intractable) problems by applying innovative statistical and numerical methods.

Optimisation methods, the bootstrap algorithm and simulation techniques including Monte Carlo methods will be introduced in relation to problems of statistical inference. You will gain experience of linking the underlying statistical concepts to practical applications of the methodology.

You will gain experience of using statistical software and interpreting its output.

This module develops the theory of the generalised linear model and its practical implementation. It builds upon and extends the linear model introduced in the Foundations of Statistics module.

The teaching extends the understanding and application of statistical methodology to the analysis of discrete (count and binary) data and survival models, which frequently occur in diverse applications. You will gain experience of using statistical software to perform exploratory data analysis and to apply generalised linear model methodology to a wide range of applications.

You will develop key statistical skills in interpreting and communicating their statistical analysis.

This module is concerned with the second main theory of statistical inference, Bayesian inference. It complements the frequentist statistical approach introduced in Statistical Inference.

This module will provide a full description of Bayesian analysis and cover popular models, such as the normal distribution and inference for categorical data.

Topics include:

• prior elicitation
• conjugate models
• marginal and predictive inference
• hierarchical models and model choice

Well known classical procedures, such as point estimation and confidence intervals, will be compared with their Bayesian counterparts.

You will also explore how computers allow the easy implementation of standard, but computationally intensive, statistical methods such as Markov chain Monte Carlo methods, to obtain samples from a posterior distribution. 

You will gain experience of linking the underlying statistical concepts to practical applications of the methodology and benefit from hands-on experience of using statistical software and interpreting its output.

Statistical Machine Learning is a topic at the interface between statistics and computer science. It concerns models that can adapt to and make predictions based on data.

The module builds on principles of statistical inference and linear regression developed in Foundations of Statistics and Frequentist Statistical Inference to introduce a variety of methods of regression and classification. This includes decision trees, support vector machines and neural networks. 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 situations.

This module is concerned with modelling and analysing data with structural dependence. We will cover two main topics:

1. time series models for analysing data that arise sequentially in time

2. multivariate data analysis in which the response is a vector of random variables rather than a single random variable

Several commonly occurring time series models will be discussed and their properties derived. Methods for model identification for real time series data will be described. 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.

For multivariate data analysis, 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 estimating and testing, based on the multivariate normal distribution
• classification of observation vectors into subpopulations using a training sample

In this course a substantial investigation will be carried out on a topic in Statistics. The study will be largely self-directed, although a supervisor will provide oversight and input where necessary.

The topic will be chosen by agreement between you and your supervisor. The topic could be based on the statistical analysis of a substantial dataset or an investigation into statistical methodology. It is expected that projects will contain an element of statistical computing.