Modelling environmental monitoring data coming from different surveys - Margalho, Luís; Menezes, Raquel; Sousa, Inês (South African Statistical Journal, 2019)
With this work we propose a spatio-temporal model for Gaussian data collected in a small number of surveys. We assume the spatial correlation structure to be the same in all surveys. In the application concerning heavy metal concentrations in mosses, the data set is dense in the spatial dimension but sparse in the temporal one, thus our model-based approach corresponds to a correlation model depending on survey orders. One advantage of this approach is its computational simplicity. An interpretation for the space-time covariance function, decomposing the overall variance of the process as the product of the spatial component variance by the temporal component variance, is introduced. A simulation study, aiming to validate the model, provided better results in terms of accuracy with the novel covariance function. Maps of predicted heavy metal concentrations and of interpolation error, for the most recent survey, are presented. Data of this kind is recurrent in environmental sciences, which is why we argue that this will be a practical tool to be used very often.