How to sample from multidimensional distributions using Gibbs sampling?

We will show how to perform multivariate random sampling using one of the Markov Chain Monte Carlo (MCMC) algorithms, called the Gibbs sampler. To start, what are MCMC algorithms and what are they based on? Suppose we are interested in generating a random variable with a distribution of, over . If we are not able to do this directly, we will be satisfied with generating a sequence of random variables, which in a sense tending to a distribution of . Build a Markov chain, for, whose stationary distribution is .