Module MATH4031: BAYESIAN STATISTICS IV

Department: MATHEMATICAL SCIENCES

MATH4031: BAYESIAN STATISTICS IV

Prerequisites

• Statistical Concepts II (MATH2041).

Corequisites

• None.

Excluded Combination of Modules

• Bayesian Statistics III (MATH3**1).

Aims

• To provide an overview of the theoretical basis for Bayesian statistics, and to offer various substantial and important practical applications of the Bayesian approach.

Content

• The Bayesian Approach: Discussion of Bayesian foundations.
• Bayesian Forecasting.
• Markov Chain Monte Carlo techniques for Bayesian computations, Bayesian graphical models, Bayes linear methods.

Learning Outcomes

• By the end of the module students will: be able to solve complex, unpredictable and specialised problems in Bayesian Statistics.
• have an understanding of specialised and complex theoretical mathematics in the field of Bayesian Statistics.
• have mastered a coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas: subjective probability and foundations of Bayesian statistics.
• Exchangeability and hierarchical modelling.
• Conditional independence and Bayesian graphical models.
• Monte Carlo inference including Gibbs sampling.
• Bayes linear methods.

• In addition students will have highly specialised and advanced mathematical skills in the following areas: Modelling, Computation.

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.
• 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