  Within the framework of Gaussian graphical models, a prior distribution for
the underlying graph is introduced to induce a block structure in the adjacency
matrix of the graph and learning relationships between fixed groups of
variables. A novel sampling strategy named Double Reversible Jumps Markov chain
Monte Carlo is developed for block structural learning, under the conjugate
G-Wishart prior. The algorithm proposes moves that add or remove not just a
single link but an entire group of edges. The method is then applied to smooth
functional data. The classical smoothing procedure is improved by placing a
graphical model on the basis expansion coefficients, providing an estimate of
their conditional independence structure. Since the elements of a B-Spline
basis have compact support, the independence structure is reflected on
well-defined portions of the domain. A known partition of the functional domain
is exploited to investigate relationships among the substances within the
compound.
