Bayesian Regression: Theory & Practice

MCMC sampling & diagnostics

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.