Module MATH4337: Uncertainty Quantification

Department: Mathematical Sciences

MATH4337: Uncertainty Quantification

Prerequisites

• Statistical Inference (MATH2671)

Corequisites

• None

Excluded Combination of Modules

• None

Aims

• To be able to design computer experiments and develop methods and procedures for the statistical analysis of modern large-scale applications in order to quantify uncertainties and perform predictions.

Content

• Introduction to Complex models of physical systems
• Emulation
• Linking the Model to Reality
• Inverse problems
• Design of computer experiments
• Sensitivity analysis

Learning Outcomes

• On the successful competition of the module, students will be able to:
• Identify and explain the nature and sources of uncertainty in large-scale applications
• Develop statistical models for the emulation of expensive computer models of physical systems.
• Explain and justify the principles of experimental design for computer models, and apply computer model design to appropriate applications.
• Explain and combine the key components of an Uncertainty Quantification for the analysis of large-scale applications.
• Implement Uncertainty Quantification methodology in a computer programming language and drawn meaningful insight and conclusions from the output.

• Students will develop advanced statistical skills and relevant mathematical skills in modelling and computation.

• Students will develop advanced skills in problem solving, critical and analytical thinking, and communicating scientific results by written reports.

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, 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 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

Summative Assessment

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