A Hybrid Model for Joint Simulation of High-Dimensional Continuous and Categorical Variables

Abstract

It is a common challenge for the geosciences to jointly model the uncertainty in continuous and categorical regionalised variables and to reproduce observed spatial correlation and complex relationships in realisations. The demand for computational efficiency in the case of high-dimensional data and large simulation domains has led practitioners to utilise approaches based on decorrelation/recorrelation and independent simulation. Among such approaches the method of min/max autocorrelation factors (MAF) has proven to be a practical technique for industrial purposes. This study presents a hybrid model for joint simulation of high-dimensional continuous and categorical variables. Continuous variables are transformed to Gaussian random functions (GRFs) via anamorphosis functions and categorical variables are obtained by truncating one or more GRFs based on the plurigaussian model. MAF factors are then derived from all GRFs. After independent simulation of MAF factors, different realisations of continuous and categorical variables are obtained via back-transformation of MAF factors followed by back-transformation for continuous and truncation for categorical variables, respectively. The proposed algorithm is illustrated through a case study.