ABSTRACT
The numerical estimation procedures are Gibbs sampling for sampling based marginal posterior means and the iterated conditional modes (ICM) algorithm for joint maximum posterior estimates. The joint posterior distribution may also be jointly maximized with respect to the parameters. Random variates can also be generated from an arbitrary distribution function by using the rejection sampling method. Gibbs sampling is a stochastic integration method that draws random variates from the posterior conditional distribution for each of the parameters conditional on fixed values of all the other parameters and the data X. The reason one would use a stochastic procedure like Gibbs sampling over a deterministic procedure like ICM is to eliminate the possibility of converging to a local mode when the conditional posterior distribution is multimodal. ICM is slightly simpler to implement than Gibbs and less computationally intensive because Gibbs sampling requires generation of random variates from the conditionals which includes matrix factorizations.
