ABSTRACT
This chapter discusses the future of the Bayesian analysis of linear models. The books of Box and Tiao, Press, and Zellner have laid the foundation for the way a Bayesian would analyze data which were generated by the linear models as those for designed experiments, mixed and random models, some time series models, and some econometric models. Many of the older books on the theory of linear models begin with a study of the so-called general linear model. The traditional models of statistical practice, the regression models and the models of designed experiments are special cases of the general linear model. The prior analysis consists of expressing prior information by either a vague improper density or a conjugate density and that if one uses a conjugate density, one may fit the hyperparameters to past data or the prior guesses of future data.
