Markov Chain Monte Carlo Methods

Abstract

The Markov Chain Monte Carlo (MCMC) methods based on the Bayes theorem are used when an a posteriori distribution does not have a tractable form and is therefore not fully known or directly usable (e.g., for maximum a posteriori parameter estimation). MCMC methods overcome intractability by drawing parameter values from known distributions and correlating these drawings until they approximately match the target distribution. MCMC methods represent a powerful class of algorithms for processing data and knowledge, which is why they are also called a "quantum leap in statistics".