STATS 731 : Bayesian Inference


2022 Semester Two (1225) (15 POINTS)

Course Prescription

A course in practical Bayesian statistical inference covering: the Bayesian approach specification of prior distributions, decision-theoretic foundations, the likelihood principle, asymptotic approximations, simulation methods, Markov Chain Monte Carlo methods, the BUGS and CODA software, model assessment, hierarchical models, application in data analysis.

Course Overview

Over the last decade, the Bayesian approach has revolutionised many areas of applied statistics such as biometrics, econometrics, market research, statistical ecology and physics. Its rise and enormous popularity today is due to the advances made in Bayesian computation through computer-intensive simulation methods. Knowledge of Bayesian procedures and software packages will become indispensable for any career in Statistics. We will be using the software package R and JAGS (or WinBUGS/OpenBUGS) for Bayesian computation, as well as some R packages. Statistics students from both theoretical and applied ends of the subject may find this course useful in a range of areas in research and industry, since Bayesian inference provides (i) a unified and compelling framework for reasoning in the presence of uncertainty; and (ii) the foundation of many popular machine-learning methods used in industry.

This course will introduce the theory of Bayesian inference, computer-intensive simulation techniques for posterior computation, and put strong emphasis on modern, applied Bayesian data analysis. Topics covered include: the Bayesian approach, conjugate prior distributions, methods for specification of prior distributions, techniques for posterior computation (incl. Laplace approximations, simulation techniques, rejection sampling, Markov chain Monte Carlo methods, and Nested Sampling), Bayesian linear and nonlinear regression models, hierarchical models, dynamic models, approaches to model comparison and selection, and model criticism.

Course Requirements

Prerequisite: STATS 210 or 225

Capabilities Developed in this Course

Capability 1: Disciplinary Knowledge and Practice
Capability 2: Critical Thinking
Capability 3: Solution Seeking
Capability 4: Communication and Engagement
Capability 5: Independence and Integrity
Capability 6: Social and Environmental Responsibilities
Graduate Profile: Master of Science

Learning Outcomes

By the end of this course, students will be able to:
  1. Understand and apply the Bayesian approach to statistical inference (Capability 1, 2, 3 and 4)
  2. Use and apply the mathematics of probability theory competently (Capability 1, 2 and 3)
  3. Understand and apply approximation and simulation techniques for posterior computation (Capability 1, 2, 3, 4 and 5)
  4. Perform applied Bayesian data analysis using a range of techniques (Capability 1, 2, 3, 4 and 5)
  5. Evaluate the goodness-of-fit of Bayesian models (Capability 1, 2, 3, 4, 5 and 6)


Assessment Type Percentage Classification
Assignments 20% Individual Coursework
Tutorials 10% Individual Coursework
Midterm Test 10% Individual Test
Final Exam 60% Individual Examination
Assessment Type Learning Outcome Addressed
1 2 3 4 5
Midterm Test
Final Exam
A minimum of 50% in the
exam along with a minimum of 50% overall is required to pass.

Special Requirements


Workload Expectations

This course is a standard 15 point course and students are expected to spend 150 hours in total over the semester for this course.

You can expect the following per week, on average: 2 hours of lectures, a 1 hour tutorial, 2 hours of reading and practicing the content and 5-7 hours of work on assignments, test preparation, and exam preparation.

Delivery Mode

Campus Experience

NOTE: A remote version of the course (including recorded lectures and online tutorial attendance) can be made available to students located overseas because of border restrictions, or those with an exemption to study remotely.

Attendance is expected at scheduled activities including lectures and tutorials, to complete components of the course. Lectures will be available as recordings. Tutorials will not be recorded but worked solutions will be available. Attendance on campus is required for the test and exam. The activities for the course are scheduled as a standard weekly timetable.

Learning Resources

Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).

Please remember that the recording of any class on a personal device requires the permission of the instructor.

A course book will be provided. Furthermore, the following textbooks are recommended and available as e-books or on desk copy at Short Loans, Kate Edger Information Commons (Level 1):

Bayesian Computation with R by Jim Albert

Bayes and Empirical Bayes Methods for Data Analysis by Carlin and Louis

Bayesian Data Analysis by Gelman, Carlin, Stern, and Rubin

The BUGS Book by Lunn, Jackson, Best, Thomas, and Spiegelhalter

Bayesian Modeling Using WinBUGS by Ioannis Ntzoufras

Bayesian Statistics: An Introduction by Peter Lee

Student Feedback

During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.

At the end of the course students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback.

Your feedback helps to improve the course and its delivery for all students.

Academic Integrity

The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed against online source material using computerised detection mechanisms.

Class Representatives

Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.


The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.

You may copy the course content for the purposes of private study or research, but you may not upload onto any third party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.

Inclusive Learning

All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.

Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website

Special Circumstances

If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.

If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page

This should be done as soon as possible and no later than seven days after the affected test or exam date.

Learning Continuity

In the event of an unexpected disruption, we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, and if disruption occurs you should refer to the university website for information about how to proceed.

The delivery mode may change depending on COVID restrictions. Any changes will be communicated through Canvas.

Student Charter and Responsibilities

The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter


Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.

In this course students may be asked to submit coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.

Published on 25/10/2021 10:30 p.m.