Winter Term 2025/2026

lecture and exercise by Dr. Guilherme de Lima Feltes

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Time and place

• Lecture: Mondays 10:00-12:00h, SR 032, Arnimallee 6

• Exercise: Tuesdays 10:00-12:00h, SR 006, Takustr. 9

• Final Exam:  TBA
• Resit Exam:  TBA

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Prerequisits: 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) would be helpful.

FU students only need to register for the course via CM (Campus Management).
Non-FU students need to register via Whiteboard.

Course Overview/ Content:

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 modelling. 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.

Teaching material will be Lecture notes and Weekly Exercise Sheets. Please look into Whiteboard for teaching material.

References

• Larry Wasserman: All of Statistics, a concise course in statistical inference
• DeGroot and Schervish: Probability and statistics, 4th edition
• José M. Bernardo, Adrian F.M. Smith: Bayesian Theory
• Leonhard Held and Daniel Sabanés Bové: Applied Statistical inference, likelihood and Bayes
• Sebastian Reich and Colin Cotter: Probabilistic forecasting and Bayesian Data Assimilation