We propose a stochastic partial differential equation to model geo-referenced data in the plane, with spatially correlated noise and a temporal log-normal evolution. Discretization in space permits us to develop the model in a finite-dimensional framework, reducing it to a set of stochastic differential equations coupled by correlated Wiener processes. The correlations are considered time-varying and stochastic, with a transformed log-normal distribution. The final model is framed within a hierarchical structure, and parameter inference is conducted jointly using Bayesian methods. The statistical methodology is illustrated by analyzing crime activity in the city of Valencia, Spain.
Calatayud et al. (Wed,) studied this question.