STAT3016 Introduction to Bayesian Data Analysis

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1 STAT3016 Introduction to Bayesian Data Analysis Course Description 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' 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. Semester and Year S Course URL Mode of Delivery On campus Prerequisites STAT2001/6039 and STAT2008/6038 Course Convener Dr Bronwyn Loong Office Location: CBE Building 26C Rm 4.23 Phone: bronwyn.loong@anu.edu.au Consultation hours: TBA Tutor Jiali Wang Student Administrators Maria Lander maria.lander@anu.edu.au 1 T H E A U S T R A L I A N N A T I O N A L U N I V E R S I T Y

2 COURSE OVERVIEW Course Learning Outcomes 1. Explain the Bayesian framework for data analysis and its flexibility in contrast to the frequentist approach; appreciate when the Bayesian approach can be beneficial. 2. Develop, analytically describe, and implement common probability models (both single and multiparameter) in the Bayesian framework (this includes models for regression analysis and generalised linear models). 3. Appreciate 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. Recognise the need to fit hierarchical models and provide the technical specifications for such models. 6. Perform Bayesian computation using Markov chain Monte Carlo methods using R. 7. Formulate a Bayesian solution to real-data problems. 8. Communicate complex statistical ideas to a diverse audience. 9. Demonstrate the necessary research skills to form a hypothesis, collect and analyse data, and reach appropriate conclusions. Research-Led Teaching The first assignment will involve review of a journal article which contrasts Bayesian and frequentist inference. 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. Technology, Software, Equipment You will be expected to perform data analyses using statistical software as part of your course work. 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 It is assumed students have a working knowledge of R from the pre-requisite course STAT2008/6038. The use of other statistical programs is permitted but support will be provided solely for R. Co-teaching This course is co-taught with STAT7016. Student Feedback All CBE courses are evaluated using Student Experience of Learning and Teaching (SELT) surveys, administered by Planning and Statistical Services at the ANU. These surveys are offered online, and students will be notified via to their ANU address when surveys are available in each course. Feedback is used for course development so please take the time to respond thoughtfully. Course feedback is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching and to improve courses across the university. For more information on student surveys at ANU and reports on feedback provided on ANU courses, visit and 2 T H E A U S T R A L I A N N A T I O N A L U N I V E R S I T Y

3 COURSE SCHEDULE (indicative) Weeks Summary of Activities 1-2 Introduction to Bayesian inference Review of probability Hoff Chapter Assessment 2-3 Bayesian inference for one parameter models 2 Assignment 1 Due 4 Monte Carlo approximation and model checking 4 5 Bayesian inference for the normal model 5 Assignment 2 Due 6 Gibbs sampling and MCMC convergence diagnostics 7 Multivariate Normal Distribution 7 Assignment 3 Due 8 Hierarchical Models 8 9 Linear Regression 9 Assignment 4 Due 10 Metropolis-Hastings Algorithm Mixed effects models 11 Assignment 5 Due Further topics in Bayesian Computation and Analysis (TBA; topics may include missing data, latent variable methods for ordinal data, computationally efficient MCMC) 1 6 7,12 Final Project Due COURSE ASSESSMENT Assessment Summary Item Title Value Due Date 1 Assignment 1 10% Wed 5 Aug 4pm 2 Assignment 2 10% Wed 19 Aug 4pm 3 Assignment 3 10% Wed 2 Sep 4pm 4 Assignment 4 10% Wed 30 Sep 4pm 5 Assignment 5 10% Wed 14 Oct 4pm 6 Final Project 50% Wed 28 Oct 4pm All assessment is mandatory and individual-based. Collaboration policy: University policies on plagiarism will be strictly enforced. You are encouraged to (orally) discuss your assignments with your classmates, but each student must write up solutions separately. Be sure that you have worked through each problem yourself and that the answers you submit are the results of your own efforts. This includes all computer code and output. For assignments involving mathematical manipulations, students can write answers by hand provided penmanship is neat; illegible answers will be marked as incorrect. For assignments requiring graphical displays, students must include the graphs in a word processor, e.g., LaTex or Word, with typed explanations about the graphs; graphs without explanations will be marked as incorrect. For assignments requiring text responses, students are strongly encouraged, but not required, to use a word processor. 3 T H E A U S T R A L I A N N A T I O N A L U N I V E R S I T Y

4 Assessment Task 1: Assignment 1 Details of task: This assignment is designed to enable students to understand and explain in detail the Bayesian framework in contrast to the frequentist approach to estimation. A selection of articles will be made available to students. Students must select one article to review and submit a report which answers a list of specific questions. Assessment Tasks 2-5: Assignments 2-5 Details of task: These assignments will require students to implement the Bayesian methods discussed in class using a statistical software package. The problems are designed to develop computational and data analyses skills. Algebraic derivations, exploration of theoretical topics and explanation of theoretical results and concepts may also be required. Assessment Task 6: Final Project Details of task: The final project will involve application of material learned in the course to a data set. Students will be given a choice of data sets to analyse and 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. Further instructions and grading guidelines will be provided later. Assignment Submission Assignments must be submitted by hardcopy. No electronic copies will be accepted. Submitted assignments must include the cover sheet available at the school office. Assignment cover sheets must not include your name, only your student ID. Please keep a copy of the assignment for your records. Assignments are to be submitted in the course box outside the school office on Level 4, Building 26C. Extensions and Penalties No late assignments will be accepted except for medical or familial emergencies, and approval for the extension must be obtained from the instructor before the due date. A late submission will result in a score of zero for the assessment task. Returning Assignments Assignments will be returned in class. Resubmission of Assignments Students may not resubmit assignments after the due date. Examinations There is no formal examination. Scaling Your final mark for the course will be based on the raw marks allocated for each assignment or examination. However, your final mark may not be the same number as produced by that formula, as marks may be scaled. Any scaling applied will preserve the rank order of raw marks (i.e. if your raw mark exceeds that of another student, then your scaled mark will exceed or equal the scaled mark of that student), and may be either up or down. 4 T H E A U S T R A L I A N N A T I O N A L U N I V E R S I T Y

5 READING LISTS Required: "A First Course in Bayesian Statistical Methods", Hoff, P. (2009). Springer: New York. (available on ereserve at the library) Recommended: "Doing Bayesian Data Analysis". Kruschke, JK. (2011). Academic Press: Massachusetts. (available on ereserve at the library) "Bayesian Data Analysis". Gelman, A., Carlin, JB., Stern, HS., Dunson, DB., Vehtari, A., and Rubin, DB. (2014). CRC Press: Florida. (available on short term loan reserve at the library) TUTORIAL AND /OR SEMINAR REGISTRATION In addition to lectures, there will be one, 1-hour tutorial each week beginning in Week 2. During tutorials, the tutor will go through the assigned tutorial questions for that week. You are also encouraged to ask questions about course material during the tutorial. Enrolment in tutorials will be completed online using the CBE Electronic Teaching Assistant (ETA). To enrol, follow these instructions: 1. Go to 2. You will see the Student Login page. To log into the system, enter your University ID (your student number) and password (your ISIS password) in the appropriate fields and hit the Login button. 3. Read any news items or announcements. 4. Select "Sign Up!" from the left-hand navigation bar. 5. Select your courses from the list. To select multiple courses, hold down the control key. On PCs, this is the Ctrl key; on Macs, it is the key. Hold this key down while selecting courses with the mouse. Once courses are selected, hit the SUBMIT button. 6. A confirmation of class enrolments will be displayed. In addition, an confirmation of class enrolments will be sent to your student account. 7. For security purposes, please ensure that you click the LOGOUT link on the confirmation page, or close the browser window when you have finished your selections. 8. If you experience any difficulties, please contact the School Office (see page 1 for contact details). 9. Students will have until 5pm July 29 July to finalise their enrolment in tutorials. After this time, students will be unable to change their tutorial enrolment. 5 T H E A U S T R A L I A N N A T I O N A L U N I V E R S I T Y

6 COMMUNICATION If necessary, the lecturers and tutors for this course will contact students on their official ANU student address. Information about your enrolment and fees from the Registrar and Student Services' office will also be sent to this address. Announcements Students are expected to check the Wattle site for announcements about this course, e.g. changes to timetables or notifications of cancellations. Notifications of emergency cancellations of lectures or tutorials will be posted on the door of the relevant room. Course URLs All course materials will be available on Wattle, the University's online learning environment. Log on to Wattle using your student number and your ISIS password. ( POLICIES The University offers a number of support services for students. Information on these is available online from 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. You can find the University s education policies and an explanatory glossary at: Students are expected to have read the Student Academic Integrity Policy before the commencement of their course. Other key policies include: Student Assessment (Coursework) Student Surveys and Evaluations 6 T H E A U S T R A L I A N N A T I O N A L U N I V E R S I T Y