Module MATH4317: Robust Bayesian Analysis

Department: Mathematical Sciences

MATH4317: Robust Bayesian Analysis

Prerequisites

• Statistical Inference (MATH2671)

Corequisites

• None

Excluded Combination of Modules

• None

Aims

• To provide advanced methodological and practical knowledge in the field of Bayesian statistics, specifically robust Bayesian methods and the foundational aspects and ramifications of various Bayesian paradigms.

Content

• Introduction to Robust Bayesian Analysis.
• Berger’s critique of p-values.
• Prior / likelihood sensitivity analysis.
• Model mis-specification.
• Robust Decisions.
• Foundations of Bayesian statistics.
• Bayes linear methods.
• Seminar classes on interpretations of probability and extensions.

Learning Outcomes

• By the end of the module students will:
• develop an understanding of the importance of robustness considerations in Bayesian statistical analyses,
• be able to elevate a typical Bayesian analysis into a robust Bayesian form, and use the acquired skills to explore its robustness,
• have a systematic and coherent understanding of the foundational theory and mathematics underlying various Bayesian paradigms, and their strengths and weaknesses,
• have acquired a coherent body of knowledge regarding Bayes linear methods,
• understand how the conceptual framework of Bayes linear methodology relates to practical implementation to real world problems.

• Students will have advanced mathematical skills in the following areas: robust Bayesian inference and the foundations of Bayesian statistics.

• Students will have advanced skills in the following areas: problem formulation and solution, critical and analytical thinking.

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.
• 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 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