[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.

Content

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 inference methods

Date and duration

Thursday, July 17, 2025, 9:00 am – 3:00 pm
Friday, July 18, 2025, 9:00 am – 3:00 pm

Audience

PhD Students and Postdocs

Further information & registration