Introductory description

This module will introduce students to modern applications of Statistics in challenging modern data analysis contexts and provide them with the theoretical underpinnings to apply these methods.

This module is available for students on a course where it is a listed option and as an Unusual Option to students who have completed the prerequisite modules.

Pre-requisites

Statistics students.

• ST218 Mathematical Statistics A; or,
• ST228 Mathematical Methods for Statistics and Probability and ST229 Probability for Mathematical Statistic.
• ST231 Linear Statistical Modelling with R.

Non-statistics students.

• ST121 Statistical Laboratory and ST232/ST233 Introduction to Mathematical Statistics.
• ST240 Linear Statistical Modelling or ST351 Linear Statistical Modelling (For Finalists)

MSc students:

• ST961 Statistical Methods and Practice and ST962 Advanced Topics in Statistics and Probability; or,
• MA907 Simulation and Machine Learning.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

The module will examine a variety of areas such as those illustrated below.

• From over-fitting to apparently complex methods which can work well, such as VC dimension and shattering sets.

• PAC bounds. Loss functions. Risk (in the learning theoretic sense) and posterior expected risk. Generalisation error.

• Supervised, unsupervised and semi-supervised learning.

• The use of distinct training, test and validation sets, particularly in the context of prediction problems.

• The Bootstrap revisited. Bags of Little Bootstraps. Bootstrap aggregation. Boosting.

• Big Data and Big Model – issues and (partial) solutions:

• The “curse of dimensionality”. Multiple testing; voodoo correlations, false-discovery rate and family-wise error rate.

• Corrections: Bonferroni, Benjamini-Hochberg.

• Sparsity and Regularisation. Variable selection; regression. Spike and slab priors. Ridge Regression. The Lasso. The Dantzig Selector.

• Concentration of measure and related inferential issues.

• MCMC in high dimensions – preconditioned Crank Nicholson; MALA, HMC. Preconditioning. Rates of convergence.

Learning outcomes

By the end of the module, students should be able to:

• Explain, critically discuss and apply fundamental concepts and analytic tools in Statistical Learning;
• Analyse and discuss issues and fundamental tools in the analysis of Big Data and Big Models;
• Implement and assess methods for prediction based on partitioning data;
• Apply fundamental tools based on sparsity, regularisation and the control of error rates to analyse large data sets.

Indicative reading list

View reading list on Talis Aspire

Subject specific skills

• Evaluate, select and apply appropriate mathematical and/or probabilist techniques.

• Demonstrate knowledge of and facility with formal probability concepts, both explicitly and by applying them to the solution of problems.

• Create structured and coherent arguments communicating them in written form. 

• Construct logical mathematical arguments with clear identification of assumptions and conclusions.

• Reason critically, carefully, and logically and derive (prove) mathematical results.

Transferable skills

• Problem solving: Use rational and logical reasoning to deduce appropriate and well-reasoned conclusions. Retain an open mind, optimistic of finding solutions, thinking laterally and creatively to look beyond the obvious. Know how to learn from failure.

• Self awareness: Reflect on learning, seeking feedback on and evaluating personal practices, strengths and opportunities for personal growth.

• Communication: Present arguments, knowledge and ideas, in a range of formats.

• Professionalism: Prepared to operate autonomously. Aware of how to be efficient and resilient. Manage priorities and time. Self-motivated, setting and achieving goals, prioritising tasks.