Aims

To gain an understanding of some of the principles of statistical inference and associated results in probability. This will deepen understanding of the fundamental precepts of inference and facilitate the assimilation of more advanced practical methodology, especially for the case when there are multidimensional parameters.

Module summary

The course builds on the foundations of inference laid in MAS2904. A variety of types of methods for inference for models with multiple parameters are established, including asymptotic methods for large samples, exact methods and computer-intensive approaches.

Outline Of Syllabus

The multivariate Normal distribution and its principal properties, especially as they relate to asymptotic likelihood methods. Maximum likelihood for multi-parameter models, including asymptotic methods for interval estimation and hypothesis testing. Revision of the idea of sufficiency and the factorization theorem and application to Cramer-Rao lower bounds and the Rao-Blackwell theorem. The bootstrap and its use to compute standard errors and interval estimates.

Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

In the event of on-campus examinations not being possible, an on-line alternative assessment will be used for written examination 1.