In practice, there are some nicer algorithms for doing Markov Chain Monte Carlo, such as Goodman & Weare's Affine Invariant sampler, as implemented in http://da

In practice, there are some nicer algorithms for doing Markov Chain Monte Carlo, such as Goodman & Weare's Affine Invariant sampler, as implemented in http://dan.iel.fm/emcee/current/ http://dan.iel.fm/emcee/current/ . This algorithm has the advantage of not needing a proposal distribution.