05-MCMC.qmd

---
title: "Bayesian Regression: Theory & Practice"
subtitle: "MCMC sampling & diagnostics"
author: "Michael Franke"
---

The success of Bayesian statistics is in large part the fruit of very clever algorithms and efficient implementations for drawing samples from complex, high-dimensional posterior distributions.
This unit covers:

- Markov Chain Monte Carlo methods, in particular: 
  + simple Metropolis-Hastings and
  + Hamiltonian Monte Carlo
- common notions and diagnostics for assessing the quality of MCMC samples, such as:
  + $\hat{R}$
  + autocorrelation
  + effective sample size
  + traceplots
  + divergent transitions
- control parameters for `brms` model fits


We also take a peak at the Stan programming language.

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