B0594
Title: Block structured Gaussian graphical models for spectrometric functional data
Authors: Alessandro Colombi - University of Milano-Bicocca (Italy)
Raffaele Argiento - Università degli Studi di Bergamo (Italy)
Lucia Paci - Universita Cattolica del Sacro Cuore (Italy) [presenting]
Alessia Pini - Universita Cattolica del Sacro Cuore (Italy)
Abstract: 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 to learn relationships between fixed groups of variables. A novel sampling strategy named Double Reversible Jumps Markov chain Monte Carlo is developed for block-structured graph 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 applied to smooth functional data, where 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 in well-defined portions of the domain. A known partition of the functional domain is exploited to investigate relationships among the substances within the compound.