- MCMC is a family of
**sampling algorithms**, which means given a distribution, these algorithms return samples according to this distribution. Many problem, bayesian posterior inference for instance, require you compute the posterior distribution P(θ|D), most of the time has no close form solution, so instead of get the actually form of P(θ|D), you sample from it, after you collect the samples, you can use these samples to estimate θ. So, MCMC is a**sampling**algorithm, not a algorithm for estimating paramters.

What is the difference between a sampling algoritms and algorithma for estimating paramters?