Module MATH4031: BAYESIAN STATISTICS IV

Department: Mathematical Sciences

MATH4031: BAYESIAN STATISTICS IV

Prerequisites

• Mathematics modules to the value of 100 credits in Years 2 and 3, with at least 40 credits at Level 3 and including Linear Algebra II (MATH2021) AND Statistical Concepts II (MATH2041).

Corequisites

• None.

Excluded Combination of Modules

• Bayesian Statistics III (MATH3341).

Aims

• To provide an overview of the theoretical basis for Bayesian statistics and an introduction to the theory and application of the Bayes linear approach.

Content

• Foundations of Bayesian statistics.
• Exponential families, sufficiency and conjugacy.
• Bayes linear methodology.
• Reading material on a topic in non-parametric Bayesian statistics.

Learning Outcomes

• Awareness of the abstract concepts of theoretical mathematics in the field of Bayesian statistics.
• Knowledge and understanding of fundamental theories of these subjects demonstrated through one or more of the following topic areas:
• subjective probability and foundations of Bayesian statistics.
• exchangeability and hierarchical modelling.
• exponential families and conjugate prior distributions.
• Bayes linear methodology.
• Knowledge and understanding of a topic in non-parametric Bayesian statistics.

• Ability to solve a range of predictable and unpredictable problems involving Bayesian statistical methodology.
• Highly specialised and advanced mathematical skills in the following areas: Modelling, Computation.
• Ability to read independently to acquire knowledge and understanding in the area of non-parametric Bayesian statistics.

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.
• Subject material assigned for independent study develops the ability to acquire knowledge and understanding without dependence on lectures.
• Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
• Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
• The end-of-year examination assesses the knowledge acquired and the ability to solve complex and specialised problems.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Four written 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