ABSTRACT
Once a posterior distribution has been derived, from the product of likelihood and prior distributions, it is important to assess how the form of the posterior distribution is to be evaluated. If single summary measures are needed then it is sometimes possible to obtain these directly from the posterior distribution either by direct maximization or analytically in simple cases. The complete sample output from the distribution is used to estimate functionals. This is certainly true when independent sample values are available. In other cases, where iterative sampling must be used, it is sometimes necessary to sub-sample the output sample. Often in disease mapping, realistic models for maps have two or more levels and the resulting complexity of the posterior distribution of the parameters requires the use of sampling algorithms. While Markov chain Monte Carlo has been extensively used for relatively small data problems, when data size becomes prohibitive then computational speed becomes critical.
