In this chapter we focus on non-stationary models. In particular, these models will show how to model the covariance using covariates and how to deal with physical barriers in the study region.

5.1 Explanatory variables in the covariance In this section we present an example of the model proposed in Ingebrigtsen et al. (2014). This example describes a way to include explanatory variables (i.e., covariates) in both of the SPDE model parameters. We will consider the parametrization used along this book and detailed in Lindgren et al. (2011).

5.1.1 Introduction First of all, we remind ourselves of the definition for the precision matrix. Restricting to α = 1 and α = 2, the precision matrix is given as follows: