Assess the key concepts of probability theory and learn how random variables and vectors and their distribution functions are defined.

Appreciate different Bayesian and frequentist approaches to statistical inference and select and justify appropriate methods for hypothesis testing.

Examine statistical modelling and regression and apply it to realistic problems and real data.

Engage with a number of computational methods that are key in modern statistics and learn to implement and apply these methods confidently.

Explore fundamental concepts of quantitative finance and statistical methods that are widely used to analyse financial data.

Further your understanding of statistical finance by engaging with modern statistical methods for analysis of financial data.

Study stochastic processes and the basic tools from stochastic analysis that provide the mathematical foundations for option pricing theory.

Gain a basic understanding of simulation, along with its uses and limitations, and the models for which basic or sophisticated simulation methods can be applied.

Understand the relative advantages of the frequentist and Bayesian approaches to statistical analysis and apply appropriate Bayesian data analyses.

Design and develop data analysis procedures using Big Data technology and use it to perform a rigorous statistical analysis.

Learn how to analyse biomedical data and design and analyse clinical trials.

Discuss key developments in contemporary statistical theory and examine analytic methods used in the development of statistical theory and methodology.

Become familiar with the most common data scientific methods and their uses and misuses.

Explore the building blocks of deep learning models, and how to design network architectures for specific applications.

Build familiarity with multivariate analysis by exploring concepts including standard multivariate notations, the covariance matrix, and multivariate normal distribution.

Build your understanding of statistical pattern recognition and machine learning and analyse state-of-art approaches.

Evaluate the strengths and weaknesses of nonparametric methods as flexible data-adaptive alternatives to parametric modelling.

Appreciate the importance of handling high dimensional datasets, through the analysis of genetics (genomics) and bioinformatics data.

Discover why survival models are fundamental to actuarial work and explore key actuarial applications.

Examine discrete time stochastic processes and associated computational algorithms and approaches.

Learn the mathematical foundations and put into practice how and why machine learning and deep learning algorithms often work so impressively well.