A Gentle Introduction to Bayesian Hierarchical Linear Regression Models

Considering the flexibility and applicability of Bayesian modeling, in this work we revise the main characteristics of two hierarchical models in a regression setting. We study the full probabilistic structure of the models along with the full conditional distribution for each model parameter. Under our hierarchical extensions, we allow the mean of the second stage of the model to have a linear dependency on a set of covariates. The Gibbs sampling algorithms used to obtain samples when fitting the models are fully described and derived. In addition, we consider a case study in which the plant size is characterized as a function of nitrogen soil concentration and a grouping factor (farm).