[ONLINE] Bayesian Statistics

This course outline ensures a logical progression from foundational concepts to advanced Bayesian modeling techniques, with a consistent emphasis on practical implementation in R.

Basic knowledge of statistics and R is required for participation.

Day 1: Fundamentals of Probability and Bayesian Concepts with Applications in R
• R recap: Probability calculations, statistical modeling, and visualization
• Overview of key R packages (e.g., Stan for Bayesian modeling)
• Introduction to probabilistic concepts: outcomes, events, probabilities
• Random variables, probability distributions, expectations, and variance
• Common distributions: Normal, Binomial, Poisson, and their applications
• The transition from probability theory to statistical modeling
• Key concepts: likelihood, prior, and posterior distributions
• Bayes’ Theorem and its role in hypothesis testing and prediction
• Practical examples demonstrating Bayesian concepts

Practical + Code Exercises
• Hands-on with R: writing scripts, using packages, and creating visualizations
• Implementation of probability concepts and distributions in R
• Coding likelihood, prior, and posterior distributions in R
• Applying Bayes’ theorem to simple problems

Day 2: Applied Bayesian Modeling and Inference
• Introduction to a simple prediction problem
• Linear regression as a framework: Frequentist vs Bayesian approaches (point estimates vs Bayesian inference).
• Analytical solutions for Bayesian linear regression with conjugate priors.
• Introduction to (Bayesian) Generalized Linear Models (GLMs), with special emphasis on logistic regression.
• Challenges in obtaining posterior distributions analytically and the need for approximation methods.
• Approximations: Maximum a posteriori (MAP) estimation and Laplace approximation.
• Benefits of uncertainty quantification through Bayesian approaches.
• Introduction to Markov Chain Monte Carlo (MCMC) methods and importance sampling for posterior approximations

Practical + Code Exercises
• Frequentist and Bayesian linear regression in R (using basic priors).
• Applying MAP and Laplace approximations to the prediction problem in R.
• Implementing MCMC and importance sampling techniques in R.
• Comparing results from MAP, Laplace approximation, and MCMC to evaluate

PhD Students and Postdocs
Credits for WFI doctoral program: 2 ECTS

Englisch

0

akademische-karrieren@ku.de

14. Februar 2025, 15:40 - 12. September 2025, 15:40

Sie müssen einen Aufnahmeantrag stellen, um in den Kurs aufgenommen zu werden. Beschreiben Sie im Feld Nachricht, warum Sie beitreten möchten. Sobald Ihr Antrag angenommen oder abgelehnt wurde, erhalten Sie eine Benachrichtigung.

Bis: 16. Juli 2025, 15:40

7

0

30. Juni 2025

17. Juli 2025, 09:00 - 18. Juli 2025, 15:00

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