Improving the Gibbs sampler

The Gibbs sampler is a simple but very powerful algorithm used to simulate from a complex high‐dimensional distribution. It is particularly useful in Bayesian analysis when a complex Bayesian model involves a number of model parameters and the conditional posterior distribution of each component given the others can be derived as a standard distribution. In the presence of a strong correlation structure among components, however, the Gibbs sampler can be criticized for its slow convergence. Here we discuss several algorithmic strategies such as blocking, collapsing, and partial collapsing that are available for improving the convergence characteristics of the Gibbs sampler.