Applied Bayesian Data Analysis with R

Dive into the world of Bayesian statistics with this comprehensive course! Unlock a powerful and intuitive framework for reasoning under uncertainty using real data and hands-on R programming. Whether you're a data scientist, social scientist, or just curious about Bayesian analysis, this course equips you with the skills to build, evaluate, and interpret Bayesian models with confidence.

We'll start by fundamentally reshaping how you understand probability, moving beyond long-run frequencies to embrace probability as a degree of belief – the core of Bayesian reasoning. Through clear explanations and practical code demonstrations, you'll learn how to update prior beliefs with new data to arrive at insightful posterior conclusions.

Next, we'll explore the computational methods that make modern Bayesian analysis scalable. Master Markov Chain Monte Carlo (MCMC) sampling, starting with the Metropolis-Hastings algorithm and progressing to advanced techniques like Hamiltonian Monte Carlo (HMC) and NUTS – the engines behind tools like Stan.

This course emphasizes practical application with the brms package in R, a user-friendly interface to Stan. You'll build Bayesian linear regressions, simulate data, check model assumptions, and effectively interpret results using familiar R syntax.

For those seeking deeper understanding, we'll delve into writing Bayesian models directly in Stan, providing complete control over model structure, likelihoods, and priors. Explore models ranging from simple linear models to non-linear growth curves and hierarchical structures.

Learn essential model validation and selection techniques, including posterior predictive checks, cross-validation, and Expected Log Predictive Density (ELPD). Diagnose convergence issues, identify divergent transitions, and follow a principled Bayesian workflow from data exploration to model validation.

By the end of this course, you will be able to:

• Think like a Bayesian: Incorporate prior knowledge and update beliefs using data.
• Confidently use MCMC methods: Fit and diagnose Bayesian models.
• Perform Bayesian regression analysis: Utilize brms and customize models using Stan.
• Simulate from priors and posteriors: Check model fit and clearly communicate uncertainty.
• Apply a principled Bayesian workflow: Solve real-world data problems from exploration to validation.