Priors on precision parameters of IGRMF models

When intrinsic Gaussian random Markov field (IGRMF) priors are assumed for random effects of a latent Gaussian model, a notable issue concerns prior elicitation for the precision hyperparameters. In fact, the structure of the precision matrix could lead to the undesired feature that the same prior for different precisions imply different marginal priors for the random effects. The work is aimed at investigating this problem following a rigorous mathematical procedure, in order to propose a new strategy and compare it to a widespread solution based on matrix scaling. Finally, an application of the proposed method to a real data problem is presented.