  Alzheimer's disease is the most common neurodegenerative disease. The aim of
this study is to infer structural changes in brain connectivity resulting from
disease progression using cortical thickness measurements from a cohort of
participants who were either healthy control, or with mild cognitive
impairment, or Alzheimer's disease patients. For this purpose, we develop a
novel approach for inference of multiple networks with related edge values
across groups. Specifically, we infer a Gaussian graphical model for each group
within a joint framework, where we rely on Bayesian hierarchical priors to link
the precision matrix entries across groups. Our proposal differs from existing
approaches in that it flexibly learns which groups have the most similar edge
values, and accounts for the strength of connection (rather than only edge
presence or absence) when sharing information across groups. Our results
identify key alterations in structural connectivity which may reflect
disruptions to the healthy brain, such as decreased connectivity within the
occipital lobe with increasing disease severity. We also illustrate the
proposed method through simulations, where we demonstrate its performance in
structure learning and precision matrix estimation with respect to alternative
approaches.
