Understanding Linchpin Variables in Markov Chain Monte Carlo

An introduction to the use of linchpin variables in Markov chain Monte Carlo (MCMC) is provided. Before the widespread adoption of MCMC methods, conditional sampling using linchpin variables was essentially the only practical approach for simulating from multivariate distributions. With the advent of MCMC, linchpin variables were largely ignored. However, there has been a resurgence of interest in using them in conjunction with MCMC methods and there are good reasons for doing so. A simple derivation of the method is provided, its validity, benefits, and limitations are discussed, and some examples in the research literature are presented.