GIBBS SAMPLER

The Gibbs sampler represents a modern statistical computing method used in theoretical and applied work. It is one of the most frequently used Markov chains. Most applications of the Gibbs sampler occur in Bayesian statistics, but it is extremely useful in frequentist (classical) models as well. Using the Gibbs sampler we can simulate the posterior probability distribution without having to express its density in the analytical form. If we can express the posterior distribution of individual parameters estimated using the conditional probability distributions, then we can gradually generate values of the individual parameters from the conditional distributions. It is the indirect way to simulate the posterior distribution of cluster, without analytical calculation and explicit expression of the probability density. This process was a great contribution to the development of the present Bayesian statistical methods. The paper aims at explaining the usage of the Gibbs sampler and at the same time introducing various methods of obtaining the required information from simulations. The problem is illustrated on the beta-binomial distribution.