Sparse regression problems, where it is usually assumed that there are
many variables and that the effects of a large subset of variables are negligible,
have become increasingly important. This paper describes the construction of
hierarchical prior distributions when the effects are considered related. These
priors allow dependence between the regression coefficients and the shrinkage to zero of different regression coefficients to be related. The properties of
these priors are discussed and applications to linear models with interactions
and generalized additive models are used as illustrations.