Bayesian Analysis Using Computer

Bayesian analysis starts with selection of a prior distribution which represents our prior knowledge about the parameter. A proper distribution on the parameter space is selected and based on this distribution posterior distribution is approximately estimated. In this paper, we will draw large samples from our prior distribution using computers. The prior sample and the likelihood function can then be utilized to generate another sample which can be considered as a sample from the posterior distribution. Gibbs sampler is another computer procedure to provide complete posterior analysis in a variety of situations. Here we briefly review this approximate methods and illustrate them by some examples.