Markov chain Monte Carlo Algorithm

MCMC is essentially Monte Carlo Method integration using Markov Chain
The key of MCMC is that we want to make the distribution approximate to a stationary distribution.

Stationary

Assume a probability distribution $Φ (t)$ at each status $X_{t}$ . When the $Φ (t)$ is same for every status and remains constant as $Φ (k)$ , we call ${Φ (k)}$ is the stationary distribution of ${X_{t}}$ .