Regression and Variable Selection

Abstract

Linear regression is one of the most widely used tools in statistics for analyzing the (linear) influence of some variables or some factors on others and thus to uncover explanatory and predictive patterns. This chapter details the Bayesian analysis of the linear (or regression) model both in terms of prior specification (Zellner’s G -prior) and in terms of variable selection, the next chapter appearing as a sequel for nonlinear dependence structures. The reader should be warned that, given that these models are the only conditional models where explicit computation can be conducted, this chapter contains a fair amount of matrix calculus. The photograph at the top of this page is a picture of processionary caterpillars, in connection (for once!) with the benchmark dataset used in this chapter.