Lectures Mon 10:15-12:00 A6/032 Dr. Vesa Kaarnioja
Exercises Tue 8:30-10:00 A6/008 Dr. Vesa Kaarnioja
Course exam Mon February 12, 2024
Make-up exam Mon March 18, 2024

General information


This course serves as an introduction to foundational aspects of modern statistical data analysis. Frequentist and Bayesian inference are presented from the perspective of probabilistic modeling. The course will consist of three main parts:

  1. Probability foundations: probability spaces, random variables, distribution of a random variable, expectation and covariance, important limit theorems and inequalities.
  2. Frequentist inference: point estimators, confidence intervals, hypothesis testing.
  3. Bayesian inference: conjugate inference, numerical models, data assimilation.


Basic set theory (inclusion, union, intersection, difference of sets), basic analysis (infinite series, calculus), matrix algebra, some knowledge of probabilistic foundations (discrete probability, Gaussian distributions) is helpful.

Completing the course

The conditions for completing this course are (1) successfully completing at least 60% of the course's exercises, (2) presenting at least 2 solutions to exercise problems in the exercise sessions, and (3) successfully passing the course exam.


Please register to the course via Campus Management (CM), then you will be automatically registered in MyCampus/Whiteboard as well. Please note the deadlines indicated there. For further information and in case of any problems, please consult the Campus Management's Help for Students.

Lecture notes

Lecture notes will be published here after each week's lecture.

Brief summary of probability theory (weeks 1–3)

Exercise sheets

Weekly exercises will be published here after each lecture.


Dr. Vesa Kaarnioja Arnimallee 6, room 212
Consulting hours: By appointment


Lecture notes of the WS22 course written by Henri Elad Altman

  • Larry Wasserman. All of Statistics: A Concise Course in Statistical Inference. Springer Science & Business Media, 2004.
  • Morris H. DeGroot and Mark J. Schervish. Probability and Statistics. 4th edition, Pearson Education, 2013.
  • José M. Bernardo and Adrian F. M. Smith. Bayesian Theory. 2nd edition, Wiley, 2007.
  • Leonhard Held and Daniel Sabanés Bové. Applied Statistical Inference: Likelihood and Bayes. Springer Science & Business Media, 2013.
  • Sebastian Reich and Colin Cotter. Probabilistic Forecasting and Bayesian Data Assimilation. Cambridge University Press, 2015.