MCMC, or Markov Chain Monte Carlo, is a class of algorithms used for sampling from probability distributions based on constructing a Markov chain that has the desired distribution as its equilibrium distribution. This technique is essential for performing Bayesian inference, especially when dealing with complex models where traditional analytical solutions are not feasible. It connects closely with diagnostics and convergence assessment to ensure reliable results, plays a significant role in R packages designed for Bayesian analysis, and underpins the concept of inverse probability by facilitating posterior sampling.
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