A Loss-Based Prior for Gaussian Graphical Models
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Gaussian graphical models play an important role in various areas such as genetics, finance, statistical physics and others. It is difficult to provide an exhaustive list of their application. They are a powerful modelling tool which allows to describe the relantionships among the variables of interest. From the Bayesian perspective, there are two sources of randomness: one is related to the multivariate distribution and the quantities that may parametrise the model, the other has to do with the underlying graph G, equivalent to describing the conditional independence structure of the model under consideration. In this paper, we will focus on assigning an objective prior on G, by using a recent loss-based approach. The new prior will be tested on simulated and real datasets and compared with other graph priors.
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