Direct minimum/maximum autocorrelation factors within the framework of a two structure linear model of coregionalisation

In this paper, we present an approach to the method of minimum/maximum autocorrelation factors (MAF) that involves the derivation of the factors in the space of the sample data. The usual approach to MAF begins with an a priori normal score transformation of each attribute. However, as the MAF method is based on principal component analysis (PCA) this initial transformation is unnecessary. Since our method derives the MAF directly in the space of the sample data, we refer to it as direct minimum/maximum autocorrelation factors (DMAF). We present a theoretical derivation of DMAF that simplifies the multi-Gaussian approach. The DMAF method is particularly advantageous when the factors are simulated using a direct simulation algorithm, as no further transformation is required. We demonstrate the DMAF method by means of the simulation of attributes from a multivariate soil data set and show that this method successfully transforms the sample attributes into uncorrelated factors for all lag spacings and is useful for multivariate simulation.