18th AIAI 2022, 17 - 20 June 2022, Greece

An Overview of MCMC Methods: From Theory to Applications

Christos Karras, Aristeidis Karras, Markos Avlonitis, Spyros Sioutas


  Markov Chain Monte Carlo techniques are used to generate samples that closely approximate a given multivariate probability distribution, with the function not having to be normalised in the case of certain algorithms such as Metropolis-Hastings. As with other Monte Carlo techniques, MCMC employs repeated random sampling to exploit the law of large numbers. Samples are generated by running a Markov Chain, which is created such that its stationary distribution follows the input function, for which a proposal distribution is used. This approach may be used for optimization tasks, for approximating solutions to non-deterministic polynomial time problems, for estimating integrals using importance sampling, and for cryptographic decoding. This paper serves as an introduction to the MCMC techniques and some of its applications.  

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