Combining information from Gaussian graphical models

Given a joint probability distribution, one can generally find its marginal components. However, it is not straightforward, or even possible, the inverse procedure. In this thesis, we shall study the wide context of combining families of distributions. In particular, we shall consider absolutely continuous distributions with respect to a product measure. The conditions for compatibility of the marginal families shall be the initial research problem to be investigated. Next, we shall classify two types of combination corresponding to the initial available information. The methodology previously introduced shall permit to lead the way to study the combination of families of multivariate normal distributions respecting some conditional independence relationships, i.e., Gaussian graphical models. Examples of combination of Gaussian graphical models and methods to estimate the parameters of the joint family of distributions shall be also provided. Eventually, we shall perform two simulation studies to assess the proposed methodology.