Module MATH4391: Nonparametric Statistics IV

Department: Mathematical Sciences

MATH4391: Nonparametric Statistics IV

Prerequisites

• Statistical Inference (MATH2711)

Corequisites

• None

Excluded Combination of Modules

• None

Aims

• To provide an overview on advanced nonparametric and distribution-free statistical methods and explain their principles through selected inferential problems both in the frequentist and the Bayesian framework.

Content

• Nonparametric density estimation.
• Nonparametric regression and smoothing techniques.
• Additive and semi-parametric models.
• Resampling methods.
• Distribution-free methods.
• Bayesian nonparametrics.

Learning Outcomes

• Identify and explain applications where nonparametric statistical approaches are appropriate.
• Explain and compare fundamental principles and basic properties of nonparametric techniques.
• Select, justify, generalise, and apply appropriate non-parametric tools for modelling and analysis of real applications and datasets.
• Implement non-parametric tools in computer programming language to generate 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 and enhance practical understanding.
• Problem classes show how to solve example problems in an ideal way, revealing also the thought processes behind such solutions.
• 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:

Regular assignments to be formatively assessed and returned with feedback. Other problems 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