3D modeling of ore grade with an approximate Bayesian approach

Since the grade of elements in a mining area has spatial correlation, its statistical analysis is impossible with the usual statistical methods. Therefore, spatial statistics methods are used in their analysis to model the spatial correlation structure and predict the unknown grade values in arbitrary locations. For prediction, including dependence structures and trend following due to contextual factors (such as topography) helps improve the accuracy of response variable forecasting. In data analysis, the small number of observations, the presence of outlier observations, or data with a highly skewed distribution, causes an inaccurate estimation of the variogram. In this article, a Bayesian approach is used for the 3D modeling of the data, and an approximate Bayesian method known as Integrated Nested Laplace Approximations (INLA) is used to fit the proposed model. Since Geostatistical data are densely indexed, to ensure fast calculations using INLA, the spatial model defined on the study area was converted into a Gaussian Markov Random Field (GMRF) using triangulation and the Stochastic Partial Differential Equation (SPDE) approach. The implementation of the INLA+SPDE method on a 3D Geostatistical data set is a new topic in the field of mining data modeling.