  We focus on the increasingly important area of sparse regression problems
where there are many variables and the effects of a large subset of these are
negligible. This paper describes the construction of hierarchical prior
distributions when the effects are considered related. These priors allow
dependence between the regression coefficients and encourage related shrinkage
towards zero of different regression coefficients. The properties of these
priors are discussed and applications to linear models with interactions and
generalized additive models are used as illustrations. Ideas of heredity
relating different levels of interaction are encompassed.
