Acceptable ergodic fluctuations and simulation of skewed distributions

摘要

Statistical fluctuations are an important part of stochastic simulation; however, the fluctuations should be reasonable and unbiased. Gaussian Simulation produces simulated values that are approximately standard normal in expected value. Minor fluctuations from a zero mean and unit variance are expected. The fluctuations will be larger when the range of correlation is large with respect to size of the domain. These fluctuations do not cause any bias in the back transformed realizations if the fluctuations are theoretically correct, that is, in keeping with the multivariate Gaussian random function model. The fluctuations may be exaggerated when certain implementation decisions are taken (ordinary kriging with a too small search neighborhood) or when the conditioning data do not follow the multivariate Gaussian model; in this case, the back transformation to original units may induce a bias in the mean in original units. This is particularly true for skewed distributions commonly encountered for geological variables. Geostatistical simulation is becoming widely used to assess risk in resource assessment. The ability to construct multiple realizations is the key feature that permits uncertainty assessment and the transfer of joint uncertainty through planning. Gaussian simulation is the simplest robust simulation approach. The practitioner should take care with many implementation decisions and checking steps. This paper documents the consequences of statistical fluctuations, poor implementation choices and the nonlinear transformation required in conventional Gaussian simulation. The problems are explained and some practical solutions are proposed.