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. Posterior sampling is a fundamental tool for exploration of posterior distributions and can provide a wide range of information about their form. Markov chain Monte Carlo methods are a set of methods which use iterative simulation of parameter values within a Markov chain. The Gibbs Sampler provides a single new value for each θ at each iteration, but requires the evaluation of a conditional distribution. On the other hand, the M-H step does not require evaluation of a conditional distribution but does not guarantee the acceptance of a new value. The Gibbs Sampler may provide faster convergence of the chain if the computation of the conditional distributions at each iteration are not time consuming.
