# STATS 331 : Introduction to Bayesian Statistics

## Science

### Course Prescription

Introduces Bayesian data analysis using the WinBUGS software package and R. Topics include the Bayesian paradigm, hypothesis testing, point and interval estimates, graphical models, simulation and Bayesian inference, diagnosing MCMC, model checking and selection, ANOVA, regression, GLMs, hierarchical models and time series. Classical and Bayesian methods and interpretations are compared.

### Course Overview

This course introduces statistics students to the Bayesian framework for performing inference. This framework is logical and consistent, and provides students with a unified view of statistics, replacing traditional approaches to hypothesis testing and parameter estimation. The course starts with a brief discussion of the history of statistics and describes how the Bayesian approach is the oldest, fell out of favour, but then made a comeback during the latter half of the 20th century. After a review of probability theory, Bayesian inference is introduced with simple toy examples to demonstrate the basic principles. The problems gradually build in complexity. In the middle of the course, Markov Chain Monte Carlo (MCMC) methods are introduced. A basic implementation of the Metropolis algorithm is presented, but most of the data analysis applications are performed using the JAGS sampler, run from within R. The latter half of the course addresses some standard data analysis situations from the Bayesian point of view using JAGS, including regression, t-tests, time series, the Dirichlet- Multinomial model, and more.  Along with the labs, these provide students with experience implementing and interpreting Bayesian analyses in common situations.  The course enables a student to perform the kind of analyses encountered in STATS 201/7/8 from a Bayesian perspective and leads to STATS 731.

### Course Requirements

Prerequisite: 15 points from STATS 201, 207, 208, BIOSCI 209

### 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

### Learning Outcomes

By the end of this course, students will be able to:
1. Describe the Bayesian and the frequentist conceptions of probability, and explain why the Bayesian one enables probability theory to be used for inference. (Capability 1 and 2)
2. Perform discrete parameter estimation in R for problems with a single unknown parameter. (Capability 1 and 2)
3. Perform basic model selection in R for problems with a single unknown parameter. (Capability 1 and 2)
4. Analytically calculate the posterior distribution for a single parameter in some simple cases involving conjugate priors. (Capability 1)
5. Explain why MCMC methods are useful. (Capability 1 and 4)
6. Describe the Metropolis algorithm. (Capability 1 and 4)
7. Use and interpret the output of inferences computed using JAGS from within R, in a range of situations. (Capability 1, 3 and 4)
8. Implement bespoke models for situations not directly covered in the course. (Capability 4 and 5)

### Assessments

Assessment Type Percentage Classification
Assignments 24% Individual Coursework
Test 20% Individual Test
Quizzes 6% Individual Coursework
Final Exam 50% Individual Examination
1 2 3 4 5 6 7 8
Assignments
Test
Quizzes
Final Exam

### Special Requirements

NA

This course is a standard 15 point course and students are expected to spend 150 hours per semester involved in each 15 point course that they are enrolled in. For this course you can expect [2] hours of lectures, a [1] hour tutorial, [4] hours of reading and thinking about the content and [3] hours of work on assignments and/or test preparation each week.

### Delivery Mode

#### Campus Experience

Attendance is expected at scheduled activities including labs to complete components of the course.
Lectures will be available as recordings. Other learning activities including labs will not be available as recordings.
The course will not include live online events. For offshore students online labs and office hours will be available.
Attendance on campus is required for the test/exam.
The activities for the course are scheduled as a standard weekly timetable.

### Learning Resources

Learning resources are lecture slides and lab materials. They will be available on Canvas.

### 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.

### Other Information

Software R will be used.

### Digital 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.

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.

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 your assessment is fair, and not compromised. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator, and if disruption occurs you should refer to the University Website for information about how to proceed.

Level 1: Delivered normally as specified in delivery mode
Level 2: You will not be required to attend in person. All teaching and assessment will have a remote option. The following activities will also have an on campus / in person option: Lectures, labs, and office hours.
Level 3 / 4: All teaching activities and assessments are delivered remotely.

### 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 .

### Disclaimer

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 you may be asked to submit your 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. The final decision on the completion mode for a test or examination, and remote invigilation arrangements where applicable, will be advised to students at least 10 days prior to the scheduled date of the assessment, or in the case of an examination when the examination timetable is published.

Published on 17/04/2021 08:21 p.m.