ABSTRACT
The basic Gibbs sampler and Metropolis algorithm can be seen as building blocks for more advanced Markov chain simulation algorithms that can work well for a wide range of problems. In Sections 12.1 and 12.2, we discuss reparameterizations and settings of tuning parameters to make Gibbs and Metropolis more efficient. Section 12.4 presents Hamiltonian Monte Carlo, a generalization of the Metropolis algorithm that includes ‘momentum’ variables so that each iteration can move farther in parameter space, thus allowing faster mixing, especially in high dimensions. We follow up in Sections 12.5 and 12.6 with an application to a hierarchical model and a discussion of our program Stan, which implements HMC for general models.
