ABSTRACT
Markov chain Monte Carlo has revolutionized modern statistical computing, especially for complex Bayesian and latent variable models. For all of its success, it dawned on the broader scientific and statistics community slowly. Markov chain Monte Carlo is not inherently a Bayesian technique. It was used for years as a way of sampling from intractable, often high-dimensional, distributions, and has widespread applications in the integration, estimation, and optimization of functions. Markov chain Monte Carlo is fundamentally a local search algorithm, and starting the algorithm from several well-dispersed initial states can help to ensure that the parameter space is fully explored. It is fairly common practice to “thin” the Markov chain in some way, for example, to retain only every mthinth step of of the converged Markov chain. Thinning is useful for reducing autocorrelation, and for reducing the amount of Markov chain Monte Carlo data one has to store and calculate with.
