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Title: A loss-based prior for Gaussian graphical models Authors:  Laurentiu Catalin Hinoveanu - University of Kent (United Kingdom) [presenting]
Fabrizio Leisen - University of Kent (United Kingdom)
Cristiano Villa - University of Kent (United Kingdom)
Abstract: Gaussian graphical models have been used across various contexts to infer the conditional independence structure arising in the sampling distribution. In the Bayesian framework, the process of learning the structure is based on model selection, where the graph prior plays an important role. In the past, the discrete uniform distribution has usually been taken as the respective graph prior, but it suffers from assigning excessive mass on medium-sized graphs. Alternative priors have been proposed to alleviate this problem by considering model edge inclusions as independent Bernoulli variables, whilst also trying to foster sparse graphs. We will illustrate a graph prior based on a methodology involving loss functions which has the peculiarity of being tuned to represent a large palette of prior sparsity knowledge. We show the behaviour of the prior through simulation studies and real data analysis.