Markov Chain Monte Carlo (MCMC) simulations allow for parameter estimation such as means, variances, expected values, and exploration of the posterior distribution of Bayesian models.
To assess the properties of a “posterior”, many representative random values should be sampled from that distribution.
Monte Carlo simulation is a type of simulation that relies on repeated random sampling and statistical analysis to compute the results.
This method of simulation is very closely related to random experiments, experiments for which the specific result is not known in advance.
Markov Chain Monte Carlo (MCMC) methods are very powerful Monte Carlo methods that are often used in Bayesian inference.
While "classical" Monte Carlo methods rely on computer-generated samples made up of independent observations, MCMC methods are used to generate sequences of dependent observations.