The goal of both methods seems to be to derive an estimate of a posterior/target distribution. If a process model exists which links some input parameters (which are themselves uncertain and can be described by a PDF) to an output parameter through a model equation or other computations, why would one choose one method over the other? Would both be applicable? Can one make a statement on the benefit of one method over the other with respect to the number of required draws/simulation runs in order to reach a sufficiently good approximation of the target PDF?
Solved – the difference between the Monte Carlo (MC) and Monte Carlo Markov Chain (MCMC) method
law-of-large-numbersmarkov-chain-montecarlomonte carlosimulationuncertainty
Best Answer
The short answer is: An MCMC is a MC, but not all MCs are MCMC.
The slightly longer answer: MC methods are a class of methods, of which MCMC is one possibility. Even MCMC does not uniquely define your method as there are different variations of MCMC.
You can read more in: Robert, C. P., & Casella, G. (2004). Monte Carlo statistical methods. New York: Springer.