[ONLINE] Bayesian Statistics

July 17-18, 2025 | Place: Zoom| EssentialDS

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Zum Kurs beitreten

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
Anmeldungsende: 16. Juli 2025, 15:40
Beitritt nach Bestätigung
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Minimale Teilnehmeranzahl: 7
Maximale Teilnehmeranzahl: 14
Freie Plätze:
14

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