Markov Chain Monte Carlo

Markov chain Monte Carlo (MCMC) in the form of the Gibbs sampler and the Metropolis, Metropolis-Hastings, and Metropolis-Hastings-Green algorithms, permits the simulation of any distribution on a finite-dimensional state space specified by any unnormalized density. As we shall see, when we can simulate we can also do inference.

• Updates Not `Algorithms'
• Combination of Updates
  • Stationarity
  • Composition
  • Mixing
  • Reversibility
  • State-Dependent Mixing
• The Metropolis-Hastings Update
• The Metropolis Update
• Variable-at-a-Time Metropolis-Hastings Updates
• The Gibbs Update
• The Metropolis-Hastings-Green Update
  • State-Dependent Mixing
• Why it Works