Bayesian Statistics
Seminar in Winter term 2026 / 2027
Organization
Time and location
Mo : 11:15 - 12:45 in
INF 205, SR 5
Preliminary meeting
Thursday, 15.10.2026, 11:15, SR 5
Description
This seminar gives an introduction to the fundamentals of Bayesian Statistics as well as deep insights into modern analysis techniques and their application.
Target group
Students in Mathematics (BSc, MSc, EwfM), Mathematics of Machine Learning and Data Science or Scientific Computing, with an interest in statistics, probability theory and machine learning. Participants should already have fundamentals in analysis, linear algebra and statistics (e.g. "Einführung in die Wahrscheinlichkeitstheorie und Statistik").
Presentations
Length: 60-70 minutes
Handout: 1-2 pages
Compulsory attendance
Consultation with advisor at least two weeks before the presentationTopics
Introduction and examples
Bayes risk
Hierarchical models
Model evaluation and comparison
Spike-and-slab regression
Gibbs sampling
Metropolis-Hastings sampling
Hamiltonian Monte Carlo
Variational inference
Bernstein-von-Mises theorem
PAC-Bayes: introduction
PAC-Bayes: oracle inequalities
Gaussian processes - regression
Gaussian processes - classification Literature
Gelman, Bayesian Data Analysis, 1995
Van der Vaart, Asymptotic Statistics, 1998
Robert & Casella, Monte Carlo Statistical Methods, 1999
Alquier, User-friendly Introduction to PAC-Bayes Bounds, 2024
Blei, Kucukelbir & McAuliffe, Variational Inference: A Review for Statisticians, 2017
Trabs, Jirak, Krenz & Reiß, Statistik und maschinelles Lernen, 2021
Rasmussen & Williams: Gaussian Processes for Machine Learning, 2005
Mitchell & Beauchamp: Bayesian Variable Selection in Linear Regression, Journal of the American Statistical Association, 83 (404), 1023-1032, 1988
Shao, Mathematical Statistics, 2003Other
Please register on MaMpf and on HeiCo.
The presentations will be assigned in the preliminary meeting on 15th October.
If there are already questions, please write an email to lehre-nps[at]math.uni-heidelberg.de.
