Bayesian methods

The course is an elective course within the Master’s Programme of Applied Biostatistics (M2STA). The course can be also offered as a free-standing course on advanced level.

The entry requirements of the course include a professional degree/ Bachelor's degree of at least 180 credits in health sciences, natural sciences, economics, or engineering. Further, R programming of at least 5 credits or equivalent, Introduction to biostatistics (STA110) or a course in mathematical statistics and/or probability theory of at least 9 credits or equivalent, English B/English 6 or equivalent, and Matematik 3b/3c or equivalent are required.

This course introduces regression models using Bayesian philosophy and software. The course commences with a brief refresher on probability defined in frequentist terms and a discussion on the limitations of this view when applied to unique events. Different schools of statistical thought, the distinction between confidence intervals and credible intervals, and the roles of generative models and of estimands in the scientific process are discussed.

The course develops full-probability modelling for single- and multi-parameter models with conjugate prior distributions. Comparisons between exact solutions and numerical approximations are provided to illustrate the use of numerical algorithms.

Further, Markov Chain Monte Carlo (MCMC) algorithms as a generic approaches to Bayesian modeling are introduced. The focus is on understanding the challenge of convergence in distribution, on diagnosing lack of convergence, and on remediating convergence problems.

Posterior predictive checks as a systematic method to assess model fit are described. Model comparison via information criteria is justified. Finally, stacking of multiple models is illustrated.

The unified workflow of a Bayesian analysis is illustrated in the case of generalised linear mixed models (GLMM). Some discussion on contemporary challenges and prior elicitation is provided.

On successful completion of the course the student will be able to:

Knowledge and understanding

• Explain the difference between frequentist and Bayesian concepts of probability and inference.
• Illustrate the role of prior, likelihood and posterior in Bayesian analysis, by means of conjugate priors.
• Explain the challenge of convergence in distribution of the MCMC sample towards the true posterior and list common causes of failure to converge.

Competence and skills

• Use statistical software to fit a specified model (likelihood and prior) and assess convergence in distribution.
• Prepare tables and figures that summarize the estimand(s) appropriately for inference, by manipulating the sample from the joint posterior.

Judgement and approach

• Specify posterior predictive checks to critically assess model fit.
• Discuss subjectivity in data collection, prior- and model specification in Bayesian and non-Bayesian workflows.

The course combines lectures and workshops. Course notes are provided by the teacher and will be discussed during workshops.

Language of instruction: English

The course is examined through participation in four workshops (2 credits) and an individual project with data material selected by the student, as well as an oral and written presentation of the project (5.5 credits). Completion of non-approved compulsory elements will be offered and is to be carried out according to the teacher's instructions.

If a student who has been failed twice for the same examination element wishes to change examiner before the next examination session, such a request is to be granted unless there are specific reasons to the contrary (Chapter 6 Section 22 HF).

If a student has received a certificate of disability study support from the University of Gothenburg with a recommendation of adapted examination and/or adapted forms of assessment, an examiner may decide, if this is consistent with the course’s intended learning outcomes and provided that no unreasonable resources would be needed, to grant the student adapted examination and/or adapted forms of assessment.

If a course has been discontinued or undergone major changes, the student must be offered at least two examination sessions in addition to ordinary examination sessions. These sessions are to be spread over a period of at least one year but no more than two years after the course has been discontinued/changed. The same applies to placement and internship (VFU) except that this is restricted to only one further examination session.

If a student has been notified that they fulfil the requirements for being a student at Riksidrottsuniversitetet (RIU student), to combine elite sports activities with studies, the examiner is entitled to decide on adaptation of examinations if this is done in accordance with the Local rules regarding RIU students at the University of Gothenburg.

The grading scale comprises: Pass (G) and Fail (U). Both the project and the participation in the workshops are graded Pass (G) or Fail (U). To obtain the grade Pass on the course, the grade Pass is required both on the project and on the participation in workshops.

The course evaluation is carried out in the form of an anonymous questionnaire. A compilation of the questionnaire is done by the course coordinator. The results of and possible changes to the course will be shared with students who participated in the evaluation and students who are starting the course.

Each participant needs access to a laptop (at least 8 GB RAM recommended) with the R software and an integrated development environment (such as RStudio or Positron) installed. The R libraries that will be used are based on the rstan package, which in turn requires rtools. The course material assumes familiarity with the R libraries dplyr and ggplot2.