Markov Chain Monte Carlo Methods

We have seen in Chapter 11 that the generation of random vectors is often not easy. The rejection based algorithms what we presented there are from a practical point of view limited to small dimensions up to at most 10. And there are lots of distributions that are even difficult to sample from in dimension three or four. A totally different approach is based on the fact that we always can easily construct a Markov chain that has the desired fixed multivariate distribution as its unique stationary distribution. Of course there is a price we have to pay for this simplicity: the dependence of the generated vectors.