Markov Chain Monte Carlo Simulation

Markov chain Monte Carlo (MCMC) is a simulation technique that can be used to find the posterior distribution and to sample from it. Thus, it is used to fit a model and to draw samples from the joint posterior distribution of the model parameters. The different MCMC algorithms differ in their performance in relation to speed and convergence depending on the model structure. Gibbs sampling, Metropolis–Hasting algorithm, and Hamiltonian Monte Carlo are briefly presented in a nontechnical way. The software OpenBUGS and Stan are MCMC samplers. Convergence of the chains is assessed graphically using traceplots and diagnostic statistics such as the -value or the Monte Carlo error.