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 in detail 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 both single and multiparameter probability models in the Bayesian framework.
3. Demonstrate in detail the role of the prior distribution in Bayesian inference and be able to articulate the usage of non-informative priors and conjugate priors.
4. Show high level Interpretation of Bayesian Analysis Results and perform Bayesian model evaluation and assessment.
5. Fit hierarchical models and provide thorough technical specifications for these models.
6. Perform Bayesian computation using Markov chain Monte Carlo methods using R.
7. Demonstrate how Bayesian Methods can be used to solve real world 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://go.exlibris.link/Vgf2pzV9

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). Feedback can also be provided to Course Conveners and teachers via the Student Experience of Learning & Teaching (SELT) feedback program. SELT surveys are confidential and also provide the Colleges and ANU Executive with opportunities to recognise excellent teaching, and opportunities for improvement.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Introduction to Bayesian inference; Review of probability (HoffChapters 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 ordinaldata (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 inExam Period

Tutorial Registration

Weekly tutorials will be delivered on-campus, commencing in Week 2. Tutorial registration will be available two weeks prior to the beginning of the semester and will close at the end of week 1. More details can be found 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 %	07/08/2023	27/10/2023	1,2,3,4,5,6
In Class Test 1	15 %	23/08/2023	01/09/2023	1,2,3,4
In Class Test 2	15 %	04/10/2023	16/10/2023	4,5,6,7
Assignment	25 %	18/10/2023	01/11/2023	4,5,6,7
Final Project	40 %	02/11/2023	30/11/2023	3,4,5,6,7

* 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 Integrity Rule before the commencement of their course. Other key policies and guidelines include:

• Academic Integrity Policy and Procedure
• Student Assessment (Coursework) Policy and Procedure
• Extenuating Circumstances Application
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure
• Code of practice for teaching and learning

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 Skills website. 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) and weekly tutorials all delivered on-campus. Weekly consultations with the lecturer and the tutor(s) will be conducted over Zoom.

Attendance at lectures and tutorials, while not compulsory, is expected in line with “Code of Practice for Teaching and Learning”, clause 2 paragraph (b).

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

In Class Test 1

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 test may require you to run some R code (or some other statistical software package of your choice)

Test 1 is mandatory and will be open book. The approximate duration of the test is 90 minutes. Test 1 will be held on-campus (that is, in-person and not online) during the lecture time, in Week 5. Your answers are to be written on the test paper given to you, and your test paper with your answers must be handed to the course convenor at the conclusion of the test. The test will be invigilated by the course convenor. Details of the test are to be advised no later than the beginning of teaching week 4 of the semester. Test 1 is to be done individually. Feedback on Test 1 is to be given by the end of week 6.

This class is co-taught with STAT3016. Students in STAT4116 may have an additional or alternative question to answer in Test 1.

Assessment Task 3

In Class Test 2

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

Test 2 is mandatory and will be open book. The approximate duration of the test is 2 hours. Test 2 will be held on-campus (that is, in-person and not online) during the lecture time, in Week 9. Your answers are to be written on the test paper given to you, and your test paper with your answers must be handed to the course convenor at the conclusion of the test. You may also be required to submit electronically some computer code written by you during the test. The test will be invigilated by the course convenor. Details of the test are to be advised no later than the beginning of teaching week 8 of the semester. Test 2 is to be done individually. Feedback on Test 2 is to be given by the end of week 10.

This class is co-taught with STAT3016. Students in STAT4116 may have an additional or alternative question to answer in Test 2.

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 Wednesday 18th October. The assignment is to be submitted electronically via Turnitin.

The assignment is mandatory and individual-based.

This class is co-taught with STAT3016. Students in STAT4116 may have an additional or alternative question to answer in the assignment.

Value: 25%.

Due date: Wednesday 18th 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 STAT4116. 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 2nd November. The final project is to be submitted electronically via Turnitin.

The final project is mandatory and individual-based.

Value: 40%.

Due date: Thursday 2nd 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. The University’s students are an integral part of that community. The academic integrity principle commits all students to engage in academic work in ways that are consistent with, and actively support, academic integrity, and to uphold this commitment by behaving honestly, responsibly and ethically, and with respect and fairness, in scholarly practice.

The University expects all staff and students to be familiar with the academic integrity principle, the Academic Integrity Rule 2021, the Policy: Student Academic Integrity and Procedure: Student Academic Integrity, and to uphold high standards of academic integrity to ensure the quality and value of our qualifications.

The Academic Integrity Rule 2021 is a legal document that the University uses to promote academic integrity, and manage breaches of the academic integrity principle. The Policy and Procedure support the Rule by outlining overarching principles, responsibilities and processes. The Academic Integrity Rule 2021 commences on 1 December 2021 and applies to courses commencing on or after that date, as well as to research conduct occurring on or after that date. Prior to this, the Academic Misconduct Rule 2015 applies.

 

The University commits to assisting all students to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. All coursework students must complete the online Academic Integrity Module (Epigeum), and Higher Degree Research (HDR) students are required to complete research integrity training. The Academic Integrity website provides information about services available to assist students with their assignments, examinations and other learning activities, as well as understanding and upholding academic integrity.

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

The Academic Skills website has information to assist you with your writing and assessments. The website includes information about Academic Integrity including referencing requirements for different disciplines. There is also information on Plagiarism and different ways to use source material.

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 Access 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 all ANU students