Admission requirements
Basic probability and statistics - obligatory
Regression modeling
R
Description
Bayesian inference is one of the fundamental paradigms of statistical inference. While it has a strong philosophical foundation which makes it conceptually distinct from other forms of statistical inference, it more importantly provides the theory that gives the unifying scientific foundation for the modern information sciences generally. Many inferential procedures and modern forms of information processing have their origins in Bayesian forms of thinking and analysis or can be understood as special applications or simplified forms of those. In this way it has become an essential component of the modern data scientist’s toolbox and education. Awareness of Bayesian forms of thinking is therefor also an important data scientific skill when engaging in collaborative research.
This course provides a basic introduction to Bayesian forms of inference. The concept of Bayesian belief updating is explained, with reference to Bayes theorem. The notions of prior and posterior density are discussed, as well as concepts and issues relating to prior belief specification. Basic forms and examples of Bayesian belief updating in both univariate and multivariate parameter problems are explained in detail, in particular with respect to the exponential family and basic linear regression models. Examples are discussed as well as applications of Bayesian concepts in approximate (non-Bayesian) forms of inference. We also introduce basic notions of Bayesian computation and apply these methods in examples and exercises. We introduce and discuss some key applications of Bayesian approaches to inference from the statistical literature.
Course Objectives
You can explain the basic concepts of Bayesian inference and are able to recognize these in documented statistical analyses materials.
You are able to apply basic methods of Bayesian inference in simple (data-based) examples.
You are able to interpret output and formulated conclusions (results) from applications of Bayesian analyses.
You are able to critically evaluate basic applications of and results from Bayesian analysis in simple examples and problem settings.
Timetable
In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.
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Note: Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.
Mode of instruction
Lectures and take-home exercises.
Assessment method
Written examination at end of the course.
Reading list
There is no specific books required.
The course lectures are much inspired by the structure presented in “Bayesian Biostatistics” (Lesaffre and Lawson, Wiley). We will particularly use many of the examples discussed in that book. Referencing the book can therefore be useful to understand these better. Material from other sources will be added to the course as required.
Many other good introductory textbooks exist for Bayesian statistics which are regarded as standard references in the field. Some students may also prefer these because of the different writing styles used in those texts. Two additional references stand out among others:
Bayesian Data Analysis by Gelman, Carlin, Stern and Rubin (an absolute classic);
Bayesian Methods for Data Analysis by Carlin and Louis (again a classic, but includes more links to “frequentist thinking” and the so-called “empirical Bayes” approach – in addition discusses some key application areas and case studies in detail ) Note this is the third edition: the first two editions have a different title: “Bayesian methods for Data Analysis and Empirical Bayes Methods for Data Analysis”;
Finally, for an excellent hands-on discussion of practical use of the Bayesian idea in evaluation of hypotheses in observational and trials data generally, Bayesian Approaches to Clinical Trials and Health-Care Evaluation by Spiegelhalter, Abrams and Myles is recommended reading.
Registration
As a student, you are responsible for enrolling on time through MyStudyMap.
In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.
Extensive information about the operation of MyStudyMap can be found here.
There are two enrolment periods per year:
Enrolment for the fall opens in July
Enrolment for the spring opens in December
See this page for more information about deadlines and enrolling for courses and exams.
Note:
It is mandatory to enrol for all activities of a course that you are going to follow.
Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.
Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.
Contact
b.mertens@lumc.nl
Remarks
Software
Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.