Non-separable spatio-temporal models via transformed multivariate Gaussian Markov random fields

Models that capture spatial and temporal dynamics are applicable in many scientific fields. Non-separable spatio-temporal models were introduced in the literature to capture these dynamics. However, these models are generally complicated in construction and interpretation. We introduce a class of non-separable transformed multivariate Gaussian Markov random fields (TMGMRF) in which the dependence structure is flexible and facilitates simple interpretations concerning spatial, temporal and spatio-temporal parameters. Moreover, TMGMRF models have the advantage of allowing specialists to define any desired marginal distribution in model construction without suffering from spatio-temporal confounding. Consequently, the use of spatio-temporal models under the TMGMRF framework leads to a new class of general models, such as spatio-temporal Gamma random fields, that can be directly used to model Poisson intensity for space-time data. The proposed model was applied to identify important environmental characteristics that affect variation in the abundance of Nenia tridens, a dominant species of gastropod in a well-studied tropical ecosystem, and to characterize its spatial and temporal trends, which are particularly critical during the Anthropocene, an epoch of time characterized by human-induced environmental change associated with climate and land use.