In health sciences, researchers are typically interested in estimating population parameters, such as the mean, difference of means, proportions, differences in proportions, etc. When using classical frequentist statistics, these parameters are estimated using data from one particular study. Although there is often a priori knowledge about likely values of a parameter, this knowledge is not included in the analysis of the current study. Central to Bayesian statistics is the idea that a ‘before’, a-priori, estimate of the probable value of a parameter is revised to an ‘after’, a posteriori, estimate based on new data. This idea fits in well with the way of thinking in medical decision-making. The Bayesian method offers the possibility to combine various data sources to update what is already known, while making inference about the uncertainty of the updated knowledge.

This 2-day course introduces the basics of Bayesian statistics and Bayesian thinking. The student will learn how to perform a Bayesian analysis of a proportion, a mean, and simple multiparameter models. In addition, the student will be introduced to Markov Chain Monte Carlo sampling and will gain understanding of real-world problems where the Bayesian approach is particularly useful. Special attention will be given to the interpretation of the results of a Bayesian analysis. The course consists of lectures and computer practicals. During the lectures, the application of Bayesian analysis is illustrated with examples from medical and epidemiological practice. During the computer practicals, the students will use the computer programme R to carry out Bayesian analyses.

The morning programme consists of lectures and the afternoon programme of computer practicals.

Topics day 1:

– The Bayesian versus the frequentist approach

– Basic concepts; the prior, the likelihood, the posterior

– Bayes’ rule; dichotomous, categorical and continuous version

– Elicitation of prior information

– Bayesian analysis of a dichotomous variable

– Bayesian analysis of a normally distributed continuous variable

– Sampling from the posterior, summary measures for the posterior

Topics day 2:

– Bayesian linear regression & logistic regression

– Markov chain Monte Carlo sampling; The Gibbs sampler

– Real-world examples

At the end of the course, the student is able to:

1. Understand the theoretical background of the Bayesian approach.
2. Apply Bayes’ rule to revise the prior for a probability or for a mean to a posterior estimate by using data.
3. Sample from the posterior distribution and calculate summary measures of the posterior.
4. Perform Bayesian linear and logistic regression.
5. Apply Markov Chain Monte Carlo sampling to estimate the posterior.
6. Describe possible applications of Bayesian methods.

Target audience

The course is intended for epidemiologists interested in Bayesian thinking, who want to become acquainted with performing simple Bayesian analyses.

Course prerequisites

Participants are expected to have;

1. Basic knowledge of epidemiological methods, to have completed the EpidM Regression Techniques (V30) course, or to have at least knowledge of the following topics:
   • Basic knowledge of probability theory, including: frequencies, (conditional) probabilities, bivariate probability distributions, (conditional) means and (conditional) expectations, variances;
   • Statistical tests, confidence intervals;
   • Linear and logistic regression models.
2. Basic knowledge of the statistical programming language R and the RStudio environment. This knowledge is expected to include at least the topics covered in the chapters 1-8 in the online book ‘Introduction to R and RStudio’ https://bookdown.org/introrbook/intro2r. If you participate in the course, an instruction video will be made available a few weeks in advance.

Course material

The course materials (lectures, assignments, feedback of the assignments etc) are available on Canvas, our digital learning environment. It is necessary to bring your own laptop. The documents will remain available on Canvas for at least one year.

In order to do the computer practicals, you will need:

1. R and R studio R and R studio can be downloaded for free athttps://cran.r-project.org/

Literature

 Literature will be provided during the course.

Epidemiology Master’s students are required to do the exam in order to complete this course. For other students (not enrolled in Epidemiology Master), the exam is optional and costs €160,- per registration.

Students who complete the exam with a pass grade will receive an exam statement mentioning the academic credits (ECs).

You can register for the exam on the Exams page. Registration will close 3 weeks prior to the exam.

Please note that you need to pass the exam in order to receive credits (EC).

A certificate of participation will be granted to all students who have attended at least 80% of the classes. The number of contact hours will stated on the certificate.

Only for Dutch medical specialists!

On the final day of the course, you need to sign the attendance list if you wish to obtain accreditation credits (PE-points).

To qualify for these credits, there is an attendance requirement of 100%.