The Traditional Unear Models

This chapter illustrates the Bayesian approach. It analyzes simple and multiple linear regression models, and examines nonlinear regression models. The chapter uses Winkler's method of the prior density of a future observation to set the values of the parameters of the normal-gamma prior density. To recapitulate one may either use an improper prior density or a conjugate prior density with which to express one's prior information about the parameters, and in the latter case, one may use the prior predictive density to set the values of the hyper parameters. The chapter examines Bayesian inferences for several normal populations. The Behrens-Fisher problem is the problem of comparing the means θ₁ and θ₂ of two normal populations which have distinct variances or precisions τ₁ and τ₂. The analysis of designed experiments usually consists, among other things, of an analysis of variance, which is a way to determine the effect of various factors on a response variable y.