# Advise on fitting spatio-temporal covariance in a likelihood framework based on Gaussian Random Field Method

I'm working on a spatial-temporal model as described in https://www.sciencedirect.com/science/article/pii/S1090780714002134.

I have modified this model such that I have an event at time Tk. Since Tk, the expected covariance between two points at different geographical distance changes over time (decrease).

This question is no meant to be on the details of the model, but I would like rather to ask if someone could direct me to some good material (not too technical) explaining well how to implement covariance structure in a likelihood framework. In other words how to adapt it to my model.

I have seen that a good approach can be to use a Gaussian Random Field Method to fit covariance structures (Rasmussen and Williams, 2006). Would be correct to use it also for covariance structure that change in time, other than some parameters determining the spatial pattern?

And, possibly, a tutorial on how to implement it in R or other platform.

Rasmussen, C. E. and C. K. Williams, 2006 Gaussian processes for machine learning, volume 1. MIT press Cambridge.