Método de seleção de preditores lineares geoestatísticos via abordagem do campo aleatório gaussiano

Abstract

Understanding a natural phenomenon and making predictions about it has been one of the major motivations of researchers and practitioners linked to the natural sciences and is undoubtedly among the fundamental reasons for science. In a geostatistical context, the problem of prediction under spatial dependence was the original question and continues to be a great challenge due to the complexity of the studied phenomena, great availability of auxiliary information, many of the spatial interpolation methods found in the literature, by the incipience of the criteria for choosing which method of interpolation would be most appropriate for each situation in particular. When only one variable is considered in the study, the answer is consecrated by the geostatistical literature: by doing kriging, since the predictors of kriging are the best linear unbiased predictors (BLUP). However, when one or more auxiliary variables are used in addition to the main variable, there is no consensus answer in the literature. Probably for these reasons, alternative techniques have been adopted by several researchers to include auxiliary variables in their studies. However, although these alternative techniques follow a practical logic, they do not guarantee that their predictors are BLUP. As consequence, the original nature of the kriging predictors is uncharacteristic, that is, they are not guaranteed to be BLUP, since their theory is not clearly defined under the non-bias and minimum variance criteria. Thus, the general objective of this work is to propose a general criterion for the selection of predictors of linear kriging that remain BLUP. This general criterion is treated in this study using the gaussian random field approach (GRFA) and although the concept of gaussian random field (GRF) is not unprecedented, the approach of Geostatistics by the GRF structure is unprecedented in its assumptions, model and results. When applying the GRFA, we reached the same predictors for the ordinary, simple and universal linear kriging, proved by the equality of the form and composition of the kriging weights in each of the linear predictor types studied. Thus, the GRFA proved to be equivalent to the classical geostatistical approach (CGA), as it was called in this text the theory of regionalized variables formalized by Matheron. For the definition of the theoretical criteria, six scenarios resulting from the combination of error partition due to spatial dependence ε^' (s_0 ) and by the existence or not of spatial autocorrelation (AC), spatial cross-correlation (CC) and simple non-spatial correlation (SC) under a geostatistical model in a GRF were defined and studied, resulting in simple criteria. It should be noted that only GRFA can explicitly, and therefore partition,ε^' (s_0 ) and perform the proposed study. Finally, a practical criterion based on the classification of a spatial dependency index SDI (%) found in the literature defines which values or range of values AC, CC and SC are strong, allowing the selection of the best predictor of linear kriging, especially when a or more auxiliary variables are introduced in the study.