Incorporating covariate information in the covariance structure of misaligned spatial data

Incorporating covariates in the second‐ structure of spatial processes is an effective way of building flexible nonstationary covariance models. Fitting these covariances requires covariates to already exist at locations where there is response data. However, studies in environmental statistics often involve covariate and response data that are misaligned in space. A common strategy to remedy this is to interpolate the covariate at locations with response data. This introduces a bias in parameters estimation and prediction. To overcome issues associated with spatial misalignment, this develops a new class of covariate‐dependent nonstationary covariance models using basis function expansions. Specifically, both covariate and response processes are represented in terms of basis systems, and the effect of the covariate is introduced on the covariance structure through a linear model between the random coefficients of basis vectors. A spike and slab prior is used to determine the structure of the association matrix between the random coefficients of the bases. The effectiveness of this prior is assessed through a simulation study. In addition, results from a real dataset show that the proposed model possesses better spatial prediction and computational advantages over other competing models.