  Collected data, which is used for analysis or prediction tasks, often have a
hierarchical structure, for example, data from various people performing the
same task. Modeling the data's structure can improve the reliability of the
derived results and prediction performance of newly unobserved data. Bayesian
modeling provides a tool-kit for designing hierarchical models. However, Markov
Chain Monte Carlo methods which are commonly used for parameter estimation are
computationally expensive. This often renders its use for many applications not
applicable. However, variational Bayesian methods allow to derive an
approximation with much less computational effort. This document describes the
derivation of a variational approximation for a hierarchical linear Bayesian
regression and demonstrates its application to data analysis.
