Markov Chain Monte-Carlo
MCMC methods have their origin in physics with the work of Metropolis, Ulam, and Rosenbluth. It was in the 1980s that they began to have a significant impact on statistics. Many MCMC algorithms and methods have been proposed and they are among the most successful approaches to computing posterior distributions.
If we use the word framework and not algorithm, it is because there is no single MCMC algorithm; instead, there are many. Multiple strategies are possible to implement it based on the problem we need to solve.
Monte-Carlo has been used for more than half a century to solve many complicated estimation problems. However, its main weakness was, as in rejection and importance sampling, its convergence in high-dimensional ...
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