The theoretical links between sequential Gaussian simulation, Gaussian truncated simulation, and probability field simulation

Sequential Gaussian simulation (sgsim), Gaussian truncated simulation (gtsi m), and probability field simulation (pfsim) are three algorithms frequentl y used for conditional stochastic simulation. They were developed independe ntly and fire seen as different algorithms in applications. This paper esta blishes that gtsim and pfsim can be bridged by a simple quantile transform between Gaussian and uniform distributions. As for the sgsim algorithm, the normal score hack-transform can be seen as a series of truncations of the simulated Gaussian field. All three algorithms are shown to be applicable t o both continuous and categorical variables. In practice, gtsim can be most often replaced by the more CPU-efficient pfsim algorithm.