ABSTRACT
This chapter reviews some recent extensions and modifications of the classic MCMC algo-
rithms described in previous chapters. Generally, researchers develop these methods to deal
with problematic estimation conditions such as multimodality, extremely high dimension,
and difficult convergence issues. This chapter also discusses some more recent developments
that speed-up the process of MCMC estimation in ways that extend standard Bayesian
stochastic estimation. These deviate from the normal orthodoxy but perhaps point towards
future development. One very promising direction described here is Hamiltonian Monte
Carlo, which is a variant of the Metropolis-Hastings algorithm. This literature is incredibly
dynamic will remain so for the next decade or more, so some of these sections merely point
at emerging literatures.
