Explaining the Gibbs Sampler

Abstract

Computer-intensive algorithms, such as the Gibbs sampler, have become increasingly popular statistical tools, both in applied and theoretical work. The properties of such algorithms, however, may sometimes not be obvious. Here we give a simple explanation of how and why the Gibbs sampler works. We analytically establish its properties in a simple case and provide insight for more complicated cases. There are also a number of examples.

Key Words:

• Data augmentation
• Markov chains
• Monte Carlo methods
• Resampling techniques