The Theoretical Links Between Sequential Gaussian Simulation, Gaussian Truncated Simulation, and Probability Field Simulation

Sequential Gaussian simulation (sgsim), Gaussian truncated simulation (gtsim), and probability field simulation (pfsim) are three algorithms frequently used for conditional stochastic simulation. They were developed independently and are seen as different algorithms in applications. This paper establishes 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 back-transform can be seen as a series of truncations of the simulated Gaussian field. All three algorithms are shown to be applicable to both continuous and categorical variables. In practice, gtsim can be most often replaced by the more CPU-efficient pfsim algorithm.