Modules

This module will introduce you to some of the most widely-used techniques in machine learning (ML). After reviewing the necessary background mathematics, we will investigate various ML methods, such as linear regression, polynomial regression and classification with logistic regression. The module covers a very wide range of practical applications, with an emphasis on hands-on numerical work using Python. At the end of the module, you will be able to formalise a ML task, choose the appropriate method to process it numerically, implement the ML algorithm in Python, and assess the method’s performance.

This module will teach the probabilistic and statistical foundations which underpin the MSc Data Analytics. This module begins by covering some of the essential theoretical notions of probability and the distributions of random variables which underpin statistical methods.  It then describes different types of statistical tests of hypotheses and addresses the questions of how to use them and when to use them. This material is essential for data analytics in applications of statistics in psychology, the life or physical sciences, business and economics.

The ability to store, manipulate and display data in appropriate ways is of great importance to data scientists. This module will introduce you to many of the most widely-used techniques in the field. The emphasis of this module on a variety of tools used interactively rather than programming as such. It will cover best practices for data visualisation as well as  various methods for preparing data for further analysis.

This module introduces you to the Python programming language. After learning about data types, variables and expressions, you will explore the most important features of the core language including conditional branching, loops, functions, classes and objects. We will also look at several of the key packages (libraries) that are widely used for numerical programming and data analysis.

This module introduces modern methods of statistical inference for small samples, which use computational methods of analysis, rather than asymptotic theory. The techniques covered in the module include non-parametric tests, bootstrap, and cross-validation. Most of these methods are now used regularly in modern business, finance, and science. Finally, the module includes the implementation of all the proposed methods with the statistics software R.

This module introduces students to methods for forecasting using both classical techniques and the latest AI-driven approaches. Students learn methods such as ARIMA, basic machine learning models, and neural networks (LSTM). In doing so, the module is centred on fundamental techniques used across industries. The module provides students with practical skills in applying forecasting methods to real-world datasets. Emphasis is placed on understanding core forecasting concepts and practical implementation using Python.

The module aims to introduce you to the Bayesian paradigm. The module will show you some of the problems with frequentist statistical methods, show you that the Bayesian paradigm provides a unified approach to problems of statistical inference and prediction, enable you to make Bayesian inferences in a variety of problems, and illustrate the use of Bayesian methods in real-life examples.

Topics include:

The Bayesian paradigm: likelihood principle, sufficiency and the exponential family, conjugate priors, examples of prior to posterior analysis, mixtures of conjugate priors, non-informative priors, two sample problems, predictive distributions, constraints on parameters, point and interval estimation,hypothesis tests, nuisance parameters.

• Linear models: use of non-informative priors, normal priors, two and three stage hierarchical models, examples of one way model, exchangeability between regressions, growth curves, outliers and influential observations.
• Approximate methods: normal approximations to posterior distributions, Laplace’s method for calculating ratios of integrals, Gibbs sampling, finding full conditionals, constrained parameter and missing data problems, graphical models. Advantages and disadvantages of Bayesian methods.
• Examples: appropriate examples will be discussed throughout the course. Possibilities include epidemiological data, randomised clinical trials, radiocarbon dating.

This module is key for students wishing to further their understanding of the visualisation techniques used in business decision processes using the powerful SAS Visual Analytics software.

You will apply the power of SAS analytics to massive amounts of data, gain valuable insights into visualisation techniques to uncover relevant patterns, and be empowered to make quicker informed decisions.

Optimisation refers to the selection of the best alternative, according to some criterion, from a set of available alternatives.

This module introduces standard models from mathematical optimisation, like network flows and linear programmes, and their use in solving real-world optimisation problems; in staff and project scheduling, commodity trading, production, and sales. Tutorials focus on modelling of real-world optimisation problems based on data, and on the use of software such as R, Excel, and Gurobi to solve optimisation problems and make better decisions.

This module will provide students with a general understanding of current applications of data analytics to finance and in particular to derivatives and investment banking. It will introduce a range of analytical tools such as volatility surface management, yield curve evolution and FX volatility/correlation management. It will also provide you with an overview of some standard tools in the field such as Python, R, Excel/VBA and the Power BI Excel functionality. Students are not expected to have any familiarity with coding or any of the topics above, as the module will develop these from scratch. It will provide you with the understanding of a field necessary to prepare for a career in finance in roles such as trading, structuring, management, risk management and quantitative positions in investment banks and hedge funds.

This module will introduce students to the elementary mathematics and analytics of investment for digital and real assets. This module will develop, from a practical approach, an understanding of the analytics of several asset classes that are currently included in investment portfolios, such as commodities, real estate, art and cryptoassets, and how these assets' statistical properties fit in the context of the portfolio. The module focuses on the concepts and characteristics of digital and real assets. It will introduce students to the mathematics of the Theory of Storage for commodities, the mathematics of indexes and uses in the real estate and art markets, trading algorithms, and cryptocurrency investment strategies such as staking, De-Fi, and non-fungible tokens. This module is particularly useful for students considering a career in financial mathematics, finance, investment management, investment banking, consultancy or asset management.

This module introduces you to several state-of-the-art methodologies for machine learning with neural networks (NNs). After discussing the basic theory of constructing and calibrating NNs, we consider various types of NN suitable for different purposes, such as convolutional NNs, recurrent NNs, autoencoders and generative adversarial networks. This module includes a wide range of practical applications; you will implement each type of network using Python for your weekly coursework assignments, and will calibrate these networks to real datasets.

This module builds on the earlier module "Machine Learning with Python", covering a number of advanced techniques in machine learning, such as dimensionality reduction, support vector machines, decision trees, random forests, and clustering. Although the underlying theoretical ideas are clearly explained, this module is very hands-on, and you will implement various applications using Python in the weekly coursework assignments.

This module addresses one of the most important “hot topics” in mathematics research – the study of networks – and is essential for understanding the characteristics and universal structural properties of complex networks. Complex networks are the outcome usually of a stochastic dynamics but they are not completely random. You will learn how to disentangle randomness from structural organisational principles of complex networks and how several major types of complex network can be described and artificially generated by mathematical models.  Networks characterise the underlying structure of a large variety of complex systems, from the Internet to social networks and the brain. This course is designed to teach students the mathematical language needed to describe complex networks, their basic properties and dynamics. The broad aim is to provide students with the key skills required fundamental research in complex networks, and necessary for application of network theory to specific network problems arising in academic or industrial environments. The students will acquire experience in solving problems related to complex networks and will learn the necessary language to formulate models of network-embedded systems.

Topics include:

• Basic concepts used in studying complex networks (e.g. adjacency matrices, degree distributions and correlations, graph distances)
• Basic tools used to study complex networks (e.g. connected components, k-cores, communities, motifs, centrality measures)
• Models for complex networks: the small world, the growing networks models and the configuration model

This module introduces students to methods for forecasting using both classical techniques and the latest AI-driven approaches. Students learn methods such as ARIMA, basic machine learning models, and neural networks (LSTM). In doing so, the module is centred on fundamental techniques used across industries. The module provides students with practical skills in applying forecasting methods to real-world datasets. Emphasis is placed on understanding core forecasting concepts and practical implementation using Python.

The module aims to introduce you to the Bayesian paradigm. The module will show you some of the problems with frequentist statistical methods, show you that the Bayesian paradigm provides a unified approach to problems of statistical inference and prediction, enable you to make Bayesian inferences in a variety of problems, and illustrate the use of Bayesian methods in real-life examples.

Topics include:

The Bayesian paradigm: likelihood principle, sufficiency and the exponential family, conjugate priors, examples of prior to posterior analysis, mixtures of conjugate priors, non-informative priors, two sample problems, predictive distributions, constraints on parameters, point and interval estimation,hypothesis tests, nuisance parameters.

• Linear models: use of non-informative priors, normal priors, two and three stage hierarchical models, examples of one way model, exchangeability between regressions, growth curves, outliers and influential observations.
• Approximate methods: normal approximations to posterior distributions, Laplace’s method for calculating ratios of integrals, Gibbs sampling, finding full conditionals, constrained parameter and missing data problems, graphical models. Advantages and disadvantages of Bayesian methods.
• Examples: appropriate examples will be discussed throughout the course. Possibilities include epidemiological data, randomised clinical trials, radiocarbon dating.

This module introduces modern methods of statistical inference for small samples, which use computational methods of analysis, rather than asymptotic theory. Some of these methods such as permutation tests and bootstrapping, are now used regularly in modern business, finance and science.

Topics include:

The techniques developed will be applied to a range of problems arising in business, economics, industry and science. Data analysis will be carried out using the user-friendly, but comprehensive, statistics package R.

• Probability density functions: the empirical cdf; q-q plots; histogram estimation; kernel density estimation.
• Nonparametric tests: permutation tests; randomisation tests; link to standard methods; rank tests.
• Data splitting: the jackknife; bias estimation; cross-validation; model selection.
• Bootstrapping: the parametric bootstrap; the simple bootstrap; the smoothed bootstrap; the balanced bootstrap; bias estimation; bootstrap confidence intervals; the bivariate bootstrap; bootstrapping linear models.

The module aims to introduce you to the Bayesian paradigm. The module will show you some of the problems with frequentist statistical methods, show you that the Bayesian paradigm provides a unified approach to problems of statistical inference and prediction, enable you to make Bayesian inferences in a variety of problems, and illustrate the use of Bayesian methods in real-life examples.

Topics include:

The Bayesian paradigm: likelihood principle, sufficiency and the exponential family, conjugate priors, examples of prior to posterior analysis, mixtures of conjugate priors, non-informative priors, two sample problems, predictive distributions, constraints on parameters, point and interval estimation,hypothesis tests, nuisance parameters.

• Linear models: use of non-informative priors, normal priors, two and three stage hierarchical models, examples of one way model, exchangeability between regressions, growth curves, outliers and influential observations.
• Approximate methods: normal approximations to posterior distributions, Laplace’s method for calculating ratios of integrals, Gibbs sampling, finding full conditionals, constrained parameter and missing data problems, graphical models. Advantages and disadvantages of Bayesian methods.
• Examples: appropriate examples will be discussed throughout the course. Possibilities include epidemiological data, randomised clinical trials, radiocarbon dating.

This module introduces modern methods of statistical inference for small samples, which use computational methods of analysis, rather than asymptotic theory. The techniques covered in the module include non-parametric tests, bootstrap, and cross-validation. Most of these methods are now used regularly in modern business, finance, and science. Finally, the module includes the implementation of all the proposed methods with the statistics software R.

This module addresses one of the most important “hot topics” in mathematics research – the study of networks – and is essential for understanding the characteristics and universal structural properties of complex networks. Complex networks are the outcome usually of a stochastic dynamics but they are not completely random. You will learn how to disentangle randomness from structural organisational principles of complex networks and how several major types of complex network can be described and artificially generated by mathematical models.  Networks characterise the underlying structure of a large variety of complex systems, from the Internet to social networks and the brain. This course is designed to teach students the mathematical language needed to describe complex networks, their basic properties and dynamics. The broad aim is to provide students with the key skills required fundamental research in complex networks, and necessary for application of network theory to specific network problems arising in academic or industrial environments. The students will acquire experience in solving problems related to complex networks and will learn the necessary language to formulate models of network-embedded systems.

Topics include:

• Basic concepts used in studying complex networks (e.g. adjacency matrices, degree distributions and correlations, graph distances)
• Basic tools used to study complex networks (e.g. connected components, k-cores, communities, motifs, centrality measures)
• Models for complex networks: the small world, the growing networks models and the configuration model

This module introduces you to several state-of-the-art methodologies for machine learning with neural networks (NNs). After discussing the basic theory of constructing and calibrating NNs, we consider various types of NN suitable for different purposes, such as convolutional NNs, recurrent NNs, autoencoders and generative adversarial networks. This module includes a wide range of practical applications; you will implement each type of network using Python for your weekly coursework assignments, and will calibrate these networks to real datasets.

This module introduces students to methods for forecasting using both classical techniques and the latest AI-driven approaches. Students learn methods such as ARIMA, basic machine learning models, and neural networks (LSTM). In doing so, the module is centred on fundamental techniques used across industries. The module provides students with practical skills in applying forecasting methods to real-world datasets. Emphasis is placed on understanding core forecasting concepts and practical implementation using Python.

This module builds on the earlier module "Machine Learning with Python", covering a number of advanced techniques in machine learning, such as dimensionality reduction, support vector machines, decision trees, random forests, and clustering. Although the underlying theoretical ideas are clearly explained, this module is very hands-on, and you will implement various applications using Python in the weekly coursework assignments.