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.