  We consider latent Gaussian fields for modelling spatial dependence in the
context of both spatial point patterns and areal data, providing two different
applications. The inhomogeneous Log-Gaussian Cox Process model is specified to
describe a seismic sequence occurred in Greece, resorting to the Stochastic
Partial Differential Equations. The Besag-York-Mollie model is fitted for
disease mapping of the Covid-19 infection in the North of Italy. These models
both belong to the class of Bayesian hierarchical models with latent Gaussian
fields whose posterior is not available in closed form. Therefore, the
inference is performed with the Integrated Nested Laplace Approximation, which
provides accurate and relatively fast analytical approximations to the
posterior quantities of interest.
