ABSTRACT
This chapter introduces the prior, posterior, and predictive analysis of the linear model. The word inference usually implies a procedure which extracts information about θ from the sample s. For the Bayesian, all inferences are based on the posterior distribution of θ, which is given by Bayes theorem. Suppose one's prior information about θ is represented by a probability density function ξ(θ, τ), θ ∈ Rp, τ > 0, then Bayes theorem combines this information with the information contained in the sample. The posterior analysis of the general linear model reveals the joint distribution of θ and τ is a normal-gamma distribution, the marginal distribution of θ is a multivariate t, and the marginal of τ a gamma if the prior of the parameters is a normal-gamma. Predictive analysis is the methodology that is developed in order to forecast future observations. Forecasting is a very important activity in business and economics, where sophisticated time series techniques are used.
