Decorrelation and Imputation Methods for Multivariate Modeling

Abstract

In most mining projects, multivariate modeling of regionalized variables has a critical impact on the final model due to complex multivariate relationships between correlated variables. In geostatistical modeling, multivariate transformations are commonly employed to model complex data relationships. This decorrelates or makes the variables independent, which enables the generation of independent models for each variable while maintaining the ability to restore multivariate relationships through a back-transformation. There are a myriad of transformation methods, however, this chapter discusses the most applied methods in geostatistical procedures. These include principal component analysis (PCA), minimum/maximum autocorrelation factors (MAF), stepwise conditional transform (SCT), and projection pursuit multivariate transform (PPMT). All these transforms require equally sampled data. In the case of unequal sampling, it is common practice to either exclude the incomplete samples or impute the missing values. Data imputation is recommended in many scientific fields as removing incomplete samples usually removes valuable information from modeling workflows. Three common imputation methods are discussed in this chapter: single imputation (SI), maximum likelihood estimation (MLE), and multiple imputation (MI). Bayesian updating (BU) is also discussed as an adaptation of MI to geostatistical analysis. MI methods are preferred in geostatistical analysis because they reproduce the variability of variables and reflect the uncertainty of missing values.