Markov Chain Monte Carlo (MCMC) Methods
In this chapter we are going to look at a method that has revolutionised statistical computing and statistical physics over the past 20 years. The principal algorithm has been around since 1953, but only when computers became fast enough to be able to perform the computations on real-world examples in hours instead of weeks did the methods become really well known. However, this algorithm has now been cited as one of the most influential ever created.
There are two basic problems that can be solved using these methods, and they are the two that we have been wrestling with for pretty much the entire book: we may want to compute the optimum solution to some objective function, or compute the posterior ...