Bayesian econometrics:conjugate analysis and rejection sampling using mathematica

Mathematica is a powerful "system for doing mathematics by computer" which runs on personal computers (Macs and MS-DOS machines), workstations and mainframes. Here we show how Bayesian methods can be implemented in Mathematica. One of the drawbacks of Bayesian techniques is that they are computation-intensive, and every computation is a little different. Since Mathematica is so flexible, it can easily be adapted to solving a number of different Bayesian estimation problems. We illustrate the use of Mathematica functions (i) in a traditional conjugate analysis of the linear regression model and (ii) in a completely nonstandard model -where rejection sampling is used to sample from the posterior