Non-monotonic Transformation for Gaussianization of Regionalized Variables: Conditional Simulation

The problem addressed in this work is the conditional simulation of a regionalized variable that is modeled as a realization of a non-monotonic transform of a Gaussian random field. As an alternative to Markov Chain Monte Carlo methods that often suffer from a slow convergence to the target distribution, we propose the use of sequential Monte Carlo approaches, with different variants of particle filtering. These variants are tested on synthetic and real datasets, to showcase their applicability and effectiveness under a proper setup of the importance sampling strategy, visiting sequence, number of particles, block size and kriging neighborhood used. The real case study, which deals with the simulation of gold grades in a porphyry copper-gold deposit, shows that the multi-Gaussian model based on a non-monotonic anamorphosis better assesses uncertainty than the traditional model based on a strictly monotonic anamorphosis, and that a moving neighborhood implementation of sequential Monte Carlo approaches can be successful, opening the door to applications to large-size problems in spatial uncertainty modeling.