# NMAK20003U Statistics A

Volume 2024/2025
Education

MSc Programme in Statistics
MSc Programme in Mathematics-Economics

Content
• Conditional distributions based on densities, including conditioning in the Gaussian distribution
• Hierarchical/mixed-effects models (theoretical and practical aspects)
• Bayesian analyses and computations, e.g., prior and posterior distributions, credible intervals, MCMC sampling
• Software for mixed-effects models and Bayesian computations
Learning Outcome

Knowledge

• Conditional densities and their relations to joint and marginal densities
• Principles behind Bayesian statistics
• Differences between fixed and random effects in mixed-effects models
• Methods for computations in posterior distributions

Skills: Ability to

• do computations with conditional and marginal densities, in particular with prior and posterior densities and with the Gaussian distribution
• carry out Bayesian estimation and inference with explicit formulas (when available) and with appropriate sampling techniques
• carry out analyses (Bayesian and frequentistic) with mixed-effects/​hierarchical models, using appropriate software

Competencies: Ability to

• identify relevant mixed-effects/​hierarchical models (for concrete data examples)
• present and discuss results from analyses statistical based on mixed-effects/​hierarchical models
• choose between principles for statistical analysis
Essential prerequisites: Probability distributions with densities, linear normal models, logistic and Poisson regression, R usage (all corresponding to courses “StatMet” and “MStat” and "Regression"). The course requires maturity at the level of MSc students in statistics; it is not an introductory statistics course.
4 hours of lectures per week for 7 weeks, 4 hours of exercises per week for 7 weeks, 3 hour test in week 9
• Category
• Hours
• Lectures
• 28
• Preparation
• 107
• Theory exercises
• 28
• Project work
• 20
• Exam Preparation
• 20
• Exam
• 3
• Total
• 206
Written
Oral
Continuous feedback during the course of the semester

Written feedback will be given on assignments.

Oral feedback will be given to students if they make presentations of exercises in class.

Credit
7,5 ECTS
Type of assessment
Continuous assessment under invigilation
Type of assessment details
The assessment is composed of two written group assignments during the course and a 3 hour individual written test by the end of the course. The group assignments count 15% each in the final assessment. Groups are expected to consist of 2-3 students, and group members must explain their contribution to the solutions handed in by the group. The individual test counts 70% in the final assessment. The test takes place during class Friday in the exam week (physical attendance, under invigilation). In order to pass, the student must hand in at least one of the group assignments, participate in the individual test, and obtain a satisfactory combined result.
Aid
All aids allowed

It is allowed to use Large Language Models (LLM)/Large Multimodal Models (LMM), e.g. ChatGPT and GPT-4, for the group assignments. The students must write whether they used these tools and for what purposes. All other aids are allowed for all exam elements.

Marking scale