The Bayesian approach to statistics assigns probability distributions to both the data and unknown parameters in the problem.  This way, we can incorporate prior knowledge on the unknown parameters before observing any data.  Statistical inference is summarised by the posterior distribution of the parameters after data collection, and posterior predictions for new observations.  The Bayesian approach to statistics is very flexible because we can describe the probability distribution of any function of the unknown parameters in the model.  Modern advances in computing have allowed many complicated models, which are difficult to analyse using ‘classical’ (frequentist) methods, to be readily analysed using Bayesian methodology.  

The aim of this course is to equip students with the skills to perform and interpret Bayesian statistical analyses.  The first part of the course is devoted to describing the fundamentals of Bayesian inference by examining some simple Bayesian models.  More complicated models will then be explored, including linear regression and hierarchical models in a Bayesian framework.  Bayesian computational methods, especially Markov Chain Monte Carlo methods will progressively be introduced as motivated by the models discussed.   Emphasis will also be placed on model checking and evaluation.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Explain the Bayesian framework for data analysis and when it can be beneficial, including its flexibility in contrast to the frequentist approach;
2. Develop, analytically describe, and implement complex single and multiparameter probability models in the Bayesian framework;
3. Demonstrate an understanding of the role of the prior distribution in Bayesian inference, and in particular the usage of non-informative priors and conjugate priors;
4. Interpret the results of a Bayesian analysis and perform Bayesian model evaluation and assessment;
5. Fit hierarchical models and provide the technical specifications for such models;
6. Perform Bayesian computation using Markov chain Monte Carlo methods using R; and,
7. Formulate a Bayesian solution to real-data problems, including forming a hypothesis, collecting and analysing data, and reaching appropriate conclusions.

Research-Led Teaching

Throughout the course, relevant journal articles may be discussed as supplementary material. The final project will involve the application of methodology learned in the course to a real data set. Students will be required to formulate their own research questions, select and implement the appropriate statistical model(s), and write a report to communicate their findings.

Field Trips

Not relevant

Required Resources

Textbook:

”A First Course in Bayesian Statistical Methods”, Hoff, P. (2009). Springer: New York. (available online via the ANU library)

https://library.anu.edu.au/record=b3727796

Technology, Software, Equipment:

You will be expected to perform data analyses using statistical software as part of your coursework. The official computer package for this course is R, which runs on Windows, MacOS and UNIX platforms. The software is free and available online through www.rproject.org: It is assumed students have a working knowledge of R from the pre-requisite course STAT2008/STAT2014. The use of other statistical programs is permitted but support will be provided solely for R.

Recommended Resources

1. ”Bayesian Data Analysis”. Gelman, A., Carlin, JB., Stern, HS., Dunson, DB., Vehtari, A., and Rubin, DB. (third edition) (2014). CRC Press: Florida. (available online via the ANU library)

https://go.exlibris.link/dlrr6Mry

2. "Statistical Rethinking: A Bayesian course with examples in R and Stan". McElreath, Richard. (second edition) (2020). Chapman and Hall. (available online via the ANU library)

https://go.exlibris.link/DnG9Jnwf

Staff Feedback

Students will be given feedback in the following forms in this course:

• written comments
• verbal comments
• feedback to whole class, groups, individuals etc

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

Other Information

As a further academic integrity control, students may be selected for a 15 minute individual oral examination of their written assessment submissions.

Any student identified, either during the current semester or in retrospect, as having used ghost writing services will be investigated under the University’s Academic Misconduct Rule.”

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Introduction to Bayesian inference; Review of probability (Hoff Chapters 1 and 2)
2	Bayesian inference for one parameter models (Hoff Chapter 3)
3	Bayesian inference for one parameter models (Hoff Chapter 3); Monte Carlo approximation and model checking (Hoff Chapter 4)	Tutorial Questions
4	Bayesian inference for the normal model (Hoff Chapter 5)
5	Gibbs sampling and MCMC convergence diagnostics (Hoff Chapter 6)	Online Test 1
6	Multivariate Normal Distribution (Hoff Chapter 7)	Tutorial Questions
7	Hierarchical Models (Hoff Chapter 8)	Tutorial Questions
8	Bayesian Linear Regression (Hoff Chapter 9 )	Tutorial Questions
9	Metropolis-Hastings Algorithm (Hoff Chapter 10)	Online Test 2
10	Mixed effects models (Hoff Chapter 11)	Tutorial Questions
11	Latent variable methods for ordinal data (Hoff Chapter 12); Bayesian models for missing data	Assignment 2 Due
12	Further topics in Bayesian Computation - computationally efficient MCMC (Variational Bayes, Hamilton Monte Carlo, Adaptive MCMC); Introduction to Bayesian Nonparametric models	Final Project Due in Exam Period

Tutorial Registration

Tutorials will be available on campus, live through scheduled Zoom sessions and as pre-recorded videos. Students should enrol in their tutorial using MyTimetable. "ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage (https://www.anu.edu.au/students/program-administration/timetabling)".

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Tutorial Questions	5 %	08/08/2022	28/10/2022	LO1 - LO6
Online Test 1	15 %	25/08/2022	05/09/2022	LO1, LO2, LO3, LO4
Online Test 2	15 %	06/10/2022	17/10/2022	LO4, LO5, LO6, LO7
Assignment	25 %	21/10/2022	03/11/2022	LO4, LO5, LO6, LO7
Final Project	40 %	03/11/2022	01/12/2022	LO3 - LO7

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines, which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information 
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the Academic Integrity . In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Participation

Course content delivery will take the form of weekly on-campus lectures (recorded and available via echo360 on Wattle), weekly tutorials, delivered in hybrid format (on campus, live through scheduled Zoom sessions and as pre-recorded videos). Weekly consultations with the lecturer and the tutor(s) will be conducted over Zoom

Assessment Task 1

Tutorial Questions

Before five of the weekly tutorial sessions, at the beginning of those weeks (see the class overview and Wattle for the exact date and time), you will submit your answers to tutorial questions online via Wattle. These will be graded for “performance” (whether you reasonably demonstrated the concepts) and not whether you got the answer correct. Each week the “performance” will be graded as 0 or 100. Feedback on tutorial submissions will given by the Friday of the same week that the submission is due.  

Value: 5%.

Assessment Task 2

Online Test 1

Online Test 1 will examine your understanding of basic Bayesian concepts. In particular, specification of a posterior distribution given a prior and likelihood function. Algebraic derivations, explanation of theoretical concepts, and interpretation of analytical results will be required. The online test may require you to run some R (or other statistical software package) code

Online Test 1 is mandatory and will be open book. The duration of Online Test 1 is to be advised. Students will be required to download the test paper, and then scan and upload their answers to the online test on Wattle. Detailed instructions on how to complete the test online will be communicated in Week 4. Online Test 1 will be held on Thursday 25th August at a time to be advised. Online test 1 is to be done individually.

Value: 15%.

Due date: Thursday 25th August (Week 5)

Assessment Task 3

Online Test 2

Online Test 2 will examine your understanding of the Gibbs sampling algorithm and its implementation in different Bayesian models. The online test may require you to run some R (or other statistical software package) code. Algebraic derivations, explanation of theoretical concepts, and interpretation of analytical results will be required.

Online Test 2 is mandatory and will be open book. The duration of Online Test 2 is to be advised. Students will be required to download the test paper, and then scan and upload their answers to the online test on Wattle. Detailed instructions on how to complete the test online will be communicated in Week 8. Online Test 2 will be held on Thursday 6th October at a time to be advised. Online test 2 is to be done individually.

Value: 15%.

Due date: Thursday 6th October (Week 9)

Assessment Task 4

Assignment

The assignment will require students to fit more complicated Bayesian models which may require implementation of the Gibbs sampling or Metropolis-Hastings algorithm. Algebraic derivations, exploration of theoretical topics and explanation of theoretical results and concepts may also be required. The assignment will be made available by the beginning of Week 8. The assignment is due on Friday 21st October. The assignment is to be submitted electronically via Turnitin.

The assignment is mandatory and individual-based.

Value: 25%.

Due date: Friday 21st October 11:59pm (Week 11)

Assessment Task 5

Final Project

The final project will involve application of material learned in the course to a real data set. Students may analyse a data set of their own choice (subject to lecturer approval)

or choose one of the data sets provided by the lecturer to analyse. Students will be required to formulate their own research question and demonstrate application of statistical methodology learned in STAT3016. Findings are to be communicated in a written report. The final project instructions will be made available by the end of Week 4. The Final Project is due on Thursday 3rd November. The final project is to be submitted electronically via Turnitin.

The final project is mandatory and individual-based.

Value: 40%.

Due date: Thursday 3rd November (first day of the Semester 2 final exam period)

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to be familiar with the academic integrity principle and Academic Misconduct Rule, uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with.

The Academic Misconduct Rule is in place to promote academic integrity and manage academic misconduct. Very minor breaches of the academic integrity principle may result in a reduction of marks of up to 10% of the total marks available for the assessment. The ANU offers a number of online and in person services to assist students with their assignments, examinations, and other learning activities. Visit the Academic Skills website for more information about academic integrity, your responsibilities and for assistance with your assignments, writing skills and study.

Online Submission

You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. Unless an exemption has been approved by the Associate Dean (Education), submission of all assignments and reports must be submitted electronically through Turnitin.

Hardcopy Submission

All assignments are to be submitted electronically via Turnitin.

Late Submission

Late submissions without an approved extension from the course convenor are not permitted. Assessment tasks submitted after the due date without an approved extension will be awarded a mark of zero.

Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

Returning Assignments

via Turnitin

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Resubmission of Assignments

Resubmission of assignments is not allowed after the due date.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Diversity and inclusion for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students