Day1

Day 1 — Bayesian Foundations and Hierarchical Models in R

This folder contains all materials for Day 1 of the Applied Bayesian Methods course

Topics

1. The Bayesian framework — Bayes' theorem, posterior inference, the likelihood principle and its connection to Bayesian updating
2. Choice of priors — weakly informative, conjugate, and regularising priors; prior predictive checks
3. Mixed effects models as Bayesian hierarchical models — random effects with different covariance structures (independent, correlated, spatial)
4. Connections to penalized regression — ridge/lasso as Bayesian shrinkage; equivalence between regularisation penalties and prior distributions
5. Temporal random effects in INLA (time permitting) — a brief applied example to bridge into Day 2

Software

• Language: R
• Primary packages: rstanarm, brms
• Supporting packages: bayesplot, loo, tidybayes, lme4 (for reference/comparison)

Folder structure

day1/
├── exercises/
├── slides/

Notes

• Slides are built with Reveal.js via Quarto (format: revealjs).
• Rendered output (e.g. *.html, *_files/) is gitignored at the repo level — do not force-add these.
• Stan models may take time to compile on first run; pre-compiled model objects (.rds) can be saved to scripts/ to speed up live demos.