NMAK20003U Statistics A

Volume 2022/2023

MSc Programme in Statistics
MSc Programme in Mathematics-Economics

  • 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


  • 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-effecs models and hierarchical models, using appropriate software

Competencies: Ability to

  • identify relevant mixed effects models and hierarchical models (for concrete data examples)
  • present and discuss results from analyses statistical based on mixed-effecs models and 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” (alternatively “MatStat” from previous years) and "Discrete Models" or "Regression"). The course requires maturity at the level of MSc students in statistics; it is not an introductory statistics course.
4 hours of lectures for 7 weeks, 4 hours of exercises per week for 8 weeks (including three multiple choice tests)
  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 118
  • Theory exercises
  • 29
  • Exam Preparation
  • 25
  • Exam
  • 6
  • Total
  • 206
Continuous feedback during the course

Written feedback will be given on voluntary assignments.

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

7,5 ECTS
Type of assessment
Continuous assessment under invigilation
Type of assessment details
The assessment is composed of two elements. The first element consists of three individual quizzes, of which the two best count a total of 50% in the final grade. The quizzes will be of one hour each and must be taken during classes (physical attendance, under surveillance). The second element is a 3 hour individual written test which counts 50% in the final grade. It must be taken during class Friday in the exam week (physical attendance, under surveillance). All aids are allowed for quizzes as well as the written test.
All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship

4 hour written test under inviligation (organized by the teacher/department). Part of the test will consist of mutiple choice questions. 



Criteria for exam assesment

The student must in a satisfactory way demonstrate that she/he has mastered the learning outcome of the course.