Undergraduate Programme and Module Handbook 2019-2020 (archived)

Module MATH4307: Object-Oriented Statistics

Department: Mathematical Sciences

MATH4307: Object-Oriented Statistics

Type	Open	Level	4	Credits	10	Availability	Not available in 2019/20	Module Cap		Location	Durham

Prerequisites

Bayesian Computation and Modelling (MATH3421)

Corequisites

None

Excluded Combination of Modules

None

Aims

To provide advanced methodological and practical knowledge of the modelling, inferential, and computational techniques needed to deal with data and mathematical objects that do not live in Euclidean spaces, and in particular with geometrical objects, and to illustrate some of the applications of these techniques.

Content

Statistics beyond R^n: manifolds, metrics, and quotient spaces. Directional statistics. Functional data analysis. Curves, surfaces, and shapes. Trees and graphs.

Learning Outcomes

Subject-specific Knowledge:

By the end of the module students will:
have a methodologically-oriented understanding of the mathematics needed to describe non-Euclidean data and objects;
have an advanced understanding of how to construct statistical models for such objects, and of the inferential techniques that may be used for them;
be able to implement such models and techniques using currently available software packages, and test their validity and performance;
have an understanding of key applications of these models and techniques;
have sufficient understanding and expertise to be able to expand their knowledge to encompass new developments in the area.

Subject-specific Skills:

Students will have advanced mathematical skills in the following areas: non-Euclidean geometry, statistical modelling, statistical computation.

Key Skills:

Students will have advanced skills in the following areas: problem formulation and solution, critical and analytical thinking, computer skills.

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.
Problem classes show how to solve example problems in an ideal way, revealing also the thought processes behind such solutions.
Computer practicals consolidate the studied material, explore theoretical ideas in practice, enhance practical understanding, and develop practical data analysis skills.
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 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/Hours
Lectures	21	Two per week in Epiphany, one in week 21	1 hour	21
Problem classes	2	Weeks 13, 17	1 hour	2
Computer practicals	2	Weeks 15, 19	1 hour	2	■
Preparation and reading				75
Total				100

Summative Assessment

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

Formative Assessment:

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

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University