In essence, Monte Carlo methods are a class of algorithms used for random sampling, while Markov Chain Monte Carlo (MCMC) is a specific type of Monte Carlo method. MCMC utilizes Markov chains to model probabilities, facilitating parameter estimation and exploration of posterior distributions, particularly in Bayesian inference. This approach combines the power of Markov chains and Monte Carlo simulations to sample from high-dimensional probability distributions, making it a valuable tool when traditional methods are inadequate.

Sources

What is the difference between the Monte Carlo (MC) and Monte Carlo Markov Chain (MCMC) method? - Cross Validated - Stack ExchangeWhat are the differences between Monte Carlo and Markov chains techniques?What is the difference between Monte Carlo simulation and Markov Chains? - QuoraA Gentle Introduction to Markov Chain Monte Carlo for Probability - MachineLearningMastery.com

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