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Estimation of stationary dependence structure parameters using only a singlerealisation of the spatial process, typically leads to inaccurate estimates andpoorly identified parameters. A common way to handle this is to fix some of theparameters, or within the Bayesian framework, impose prior knowledge. In manyapplied settings, stationary models are not flexible enough to model theprocess of interest, thus non-stationary spatial models are used. However, moreflexible models usually means more parameters, and the identifiability problembecomes even more challenging. We investigate aspects of estimation of aBayesian non-stationary spatial model for annual precipitation usingobservations from multiple years. The model contains replicates of the spatialfield, which increases precision of the estimates and makes them less priorsensitive. Using R-INLA, we analyse precipitation data from southern Norway,and investigate statistical properties of the replicate model in a simulationstudy. The non-stationary spatial model we explore belongs to a recentlyintroduced class of stochastic partial differential equation (SPDE) basedspatial models. This model class allows for non-stationary models withexplanatory variables in the dependence structure. We derive conditions tofacilitate prior specification for these types of non-stationary spatialmodels.

Estimation of a non-stationary model for annual precipitation in southern Norway using replicates of the spatial field