For a very long time there has been a stark dichotomy between the classical (or frequentist) and Bayesian (or subjectivist) approaches to statistical inference, the former being the more commonly followed approach is that in real world applications in statistics and econometrics. A distinctive feature of the Bayesian approach is that it involves the systematic use of prior information in addition to sample information, through the Bayes theorem. In recent years the Bayesian approach has gone beyond merely replicating the well known results of the classical approach in Bayesian setting to working out solutions to problems that were once regarded as intractable. Monte Carlo integration techniques have enabled researchers to deal with some complex problems in the Bayesian context. Bayesian procedures have been found to be useful in solving many decision problems. Applications of the Bayesian methodology have become quite extensive and special in economics and finance.