Variance partitioning priors for latent gaussian models

Variance partitioning priors have recently been proposed in the context of Bayesian hierarchical models. They are defined as those priors that make use of a reparametrization of the variance parameters into a total variance and a set of proportions. This work proposes a standardization procedure to accommodate variance partitioning priors into a large class of models, namely latent Gaussian models. The standardization procedure to be applied on the model effects guarantees an intuitive interpretation for the new parameters. The procedure acknowledges how the interpretation of variance contributions as intended by the user can differ between fixed and random effects. Particular attention is given to the special class of intrinsic Gaussian Markov random fields, which are popularly used to model spatial and temporal correlation. The benefits of the proposal are validated through simulations, which have confirmed the practical relevance of the standardization procedure. The importance of the contribution lies in the possibility of fully exploiting prior information through variance partitioning priors, which is particularly beneficial to those applications and fields that require complex modelling structures. This advantage is exemplified in the context of species distribution models used in ecology, which are usually composed by different fixed and random effects.