ABSTRACT
This chapter introduces one commonplace example of Fortuna and Minerva’s cooperation: the estimation of posterior probability distributions using a stochastic process. It explains the concept behind Gibbs sampling. The precise algorithm King Markov used is a special case of the general Metropolis algorithm from the real world. The improvement arises from adaptive proposals in which the distribution of proposed parameter values adjusts itself intelligently, depending upon the parameter values at the moment. The Metropolis algorithm and Gibbs sampling are highly random procedures. Trace plots are a natural way to view a chain, but they are often hard to read, because once plotting lots of chains over one another is started, the plot can look very confusing and hide pathologies in some chains. Markov chain Monte Carlo is a highly technical and usually automated procedure.
