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MATH4287: High-Dimensional Statistics

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Type	Open
Level	4
Credits	10
Availability	Available in 2023/24
Module Cap	None.
Location	Durham
Department	Mathematical Sciences

Prerequisites

Statistical Inference (MATH2711)

Corequisites

None

Excluded Combinations of Modules

None

Aims

To provide advanced methodological skills for the analysis of high-dimensional data, spanning the arc from the theoretical underpinning of the methods to the practical application on real data.

Content

Multivariate statistics: principal component analysis, cluster analysis, and related methods.
Dimension reduction: regularized regression techniques.

Learning Outcomes

Subject-specific Knowledge:

A thorough understanding and working knowledge of advanced statistical methods for multivariate data;
An appreciation of the wider concepts that such methods are built on, allowing straightforward understanding of yet unseen methods;
The intuition to distinguish supervised and unsupervised learning scenarios, and which specific methods to apply in particular situations.

Subject-specific Skills:

Students will have advanced mathematical skills in the following areas: modelling, computation.

Key Skills:

Students will have advanced skills in the following areas: problem solving, synthesis of data, critical and analytical thinking, report writing.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
Computer practicals consolidate the studied material and enhance practical understanding.
Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
Formative assessments provide feedback to guide students in the correct development of their knowledge and skills in preparation for the summative assessment.
The written project report assesses the ability to implement the concepts introduced in the module using statistical software, to apply them in the analysis of a realistic problem, and to report scientific outputs in a clear and structured way.
The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total	Monitored
Lectures	21	Two per week in weeks 1-10, one in week 21	1 hour	21
Computer Practicals	4	Weeks 2, 4, 6, 8	1 hour	4	Yes
Preparation and reading				75
Total				100

Summative Assessment

Component: Examination		Component Weighting: 80%
Element	Length / Duration	Element Weighting	Resit Opportunity
Written examination	2 hours	100

Component: Coursework		Component Weighting: 20%
Element	Length / Duration	Element Weighting	Resit Opportunity
Mini project report		100

Formative Assessment

Two written or electronic assignments to be assessed and returned.Other assignments are set for self-study and complete solutions are made available to students.

More information

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