A framework for conditional simulation of nonstationary non-Gaussian random field and multivariate processes. (15th January 2023) - Hong, H.P.; Xiao, M.Y.; Cui, X.Z.; Liu, Y.X.
Highlights: Proposed a new conditional simulation framework for the nonstationary non-Gaussian field/processes. Framework is applicable for given covariance or time–frequency information, and marginal distribution. Algorithms used are efficient for conditional simulation as they reuse the unconditional samples. Showed the application and effectiveness of the framework through several examples. Abstract: We propose a conditional simulation framework for the nonstationary/nonhomogeneous non-Gaussian/Gaussian field and multivariate processes. There are three distinct stages within the proposed framework. The first one is to sample directly the unconditional nonstationary non-Gaussian field or multivariate processes without resorting to the underlying Gaussian characteristics. The second stage maps the unconditional samples and the conditions (i.e., observations) to the Gaussian space and uses them to find the conditional mean and covariance. In the final stage, the conditional samples by considering the effect of the conditioning are generated in Gaussian space and mapped back to the original non-Gaussian field. The efficiency of the framework relies on the efficient unconditional simulation algorithms (i.e., the iterative rank-dependent shuffling algorithm, and the iterative power and amplitude correction algorithm), and the reuse of the unconditional samples for the conditional simulation. The conditional samples match the conditional mean and conditional variance–covariance. The framework can directly apply to the random field and multivariate processes defined by the marginal probability distribution function and the covariance-variance information, or the time–frequency dependent PSD function. The framework is illustrated using several examples.