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What is Markov Chain Monte Carlo?

Markov chain Monte Carlo

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Metropolis–Hastings algorithm

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Markov Chain Monte Carlo (MCMC) is a field of stochastic algorithms used for sampling from arbitrary distributions. It has numerous applications in science and technology. MCMC algorithms are typically time-reversible and satisfy the detailed-balance condition, similar to physical systems in thermal equilibrium. These algorithms explore sample space slowly due to diffusive dynamics. Non-reversible MCMC algorithms with non-equilibrium dynamics can achieve significant speed-ups by exactly reproducing the target equilibrium states of reversible Markov chains. However, analyzing these algorithms is challenging, resulting in a scarcity of exact results. The "lifted" TASEP model is introduced as a paradigm for lifted non-reversible Markov chains, which leads to faster relaxation than the KPZ universality class . MCMC allows complex and multidimensional distributions to be sampled, and it applies to simpler cases as well. It is based on Markov Chains and the Metropolis-Hastings Algorithm, and it is used in inference and decision analysis . The core idea of MCMC methods is to construct a transition rule for a reversible Markov chain whose equilibrium distribution is the desired target distribution . Nonparametric involutive Markov chain Monte Carlo (NP-iMCMC) is a method for constructing MCMC inference algorithms for nonparametric models expressible in universal probabilistic programming languages .

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Journal Article•DOI Configurational and Orientational Bias Monte Carlo Talha Burki 11 Feb 2023-Wiley StatsRef: Statistics Reference Online	The paper does not provide a direct answer to the query "what is Markov Chain Monte Carlo?"
Lifted TASEP: a Bethe ansatz integrable paradigm for non-reversible Markov chains Fabian H. L. Essler, Werner Krauth - Show less +1 more 22 Jun 2023	Markov-chain Monte Carlo (MCMC) is a field of stochastic algorithms used for sampling. The paper discusses non-reversible MCMC algorithms and their applications.
Book Chapter•DOI Markov Chain Monte Carlo 01 Jan 2023 1 Citations	Markov Chain Monte Carlo (MCMC) is a clever way to obtain samples from almost any arbitrary distributions.
Open access•Posted Content•DOI Lifted TASEP: a Bethe ansatz integrable paradigm for non-reversible Markov chains 22 Jun 2023	Markov Chain Monte Carlo (MCMC) is a field of stochastic algorithms used for sampling. The paper discusses non-reversible MCMC algorithms and their applications.

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