Course syllabus for Mathematics of causal inference

Matematik för kausal inferens

Specific entry requirements

At least the grade G (Pass) for the courses "Theory of statistical inference" and "Probability Theory".

Outcomes

The course aims to give the student an introduction to the mathematical foundations of modern causal inference. Emphasis is placed on mathematical concepts, derivations, and proofs.

Upon completion of the course, the student should be able to:

Regarding knowledge and understanding

• Explain and mathematically derive key causal inference target parameters, such as marginal and conditional causal effects, controlled direct effects, and natural direct effects, and discuss their interpretation and relevance in different contexts.
• Describe, with mathematical rigour, common sources of bias (e.g., exposure-outcome confounding, mediator-outcome confounding, selection bias, and truncation by death) and their implications for causal effect estimation.

Regarding competence and skills

• Implement modern causal inference methods, including instrumental variables, propensity scores, doubly robust estimation, and E-values, and explain, with mathematical rigour, how these methods can be used to mitigate biases in the estimation of causal target parameters.

Regarding judgement and approach

• Critically evaluate the assumptions, strengths, and limitations of different causal inference methods in applied research.
• Justify and defend methodological choices for causal effect estimation in diverse research settings, considering both theoretical and practical constraints.

Content

The course covers mathematical concepts, derivations, and proofs underlying modern causal inference.

Teaching methods

The forms of teaching and learning are seminars, self-studies, and group learning. The course emphasises active learning.

Examination

The grading decision will be based on the examiner’s assessment of the student’s performance during the oral presentations in seminars, active participation in group discussions, and individual discussions with the examiner.

Compulsory participation
All seminars are compulsory.

The examiner assesses if and, in that case, how absence from compulsory components can be compensated. The student must participate in all compulsory parts or compensate for absence in accordance with the examiner's instructions, in order to pass the course. Absence from a compulsory activity may result in the student not being able to compensate the absence until the next time the course is given.

Limit to the number of examinations
A student who does not pass an examination at their first attempt is entitled to participate in five additional examination sessions. If the student does not pass after four examinations, he/she is recommended to retake the course at the next regular course occasion, and may, after that, participate in two more examination sessions. If the student has failed six examinations, no additional examination sessions are provided.

Physically attending or otherwise commencing an examination is regarded as an examination session. Handing in a blank exam is considered taking part in an examination session. An examination, for which the student registered but did not participate, is not counted as an examination session.

Adaption of examination
If there are special grounds, or a need for adaptation for a student with a disability, the examiner may decide to deviate from the syllabus' regulations on the examination form or the possibility of supplementation or exemptions from compulsory sections of the course. Content and learning outcomes as well as the level of expected skills, knowledge and abilities may not be changed, removed, or reduced.

Other directives

The course language is English.

Literature and other teaching aids

Study material and reference articles will be provided during the course.

Recommended literature

- Pearl, J. (2009). Causality. Cambridge university press.

- Hernán MA, Robins JM (2023). Causal Inference: What If. Boca Raton: Chapman & Hall/CRC.