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When I want to estimation parameter of beta distribution and I have large amount of samples, what would be the advantage of using MCMC over calculating these two parameters (alpha and beta) of beta distribution by simple counting?

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    $\begingroup$ MCMC is not an estimation method but rather a simulation technique used to simulate complex distributions as for instance Bayesian posteriors. In the present context of estimating the parameters of an exponential family, without further details about a specific prior distribution, there is no clear motivation for using an MCMC algorithm. $\endgroup$ – Xi'an Apr 15 at 9:47

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