Modeling and Simulation of Stochastic Data

Abstract

Stochastic data appear as basic components in reliability analysis and geostatistics. It is rarely emphasized that the multivariate probability distributions underlying random vectors (or processes, fields) are very difficult to construct theoretically, to estimate empirically, and to simulate numerically. This paper discusses the modeling and simulation of non-Gaussian random vectors, highlighting some useful geotechnical applications, important limitations, and outstanding challenges. Discussion is restricted to translation vectors, although emerging techniques that can potentially simulate a wider class of non-Gaussian random vectors would be briefly introduced for completeness. The translation approach is quite natural and takes advantage of the practicality, theoretical generality, and simulation speed associated with the multivariate Gaussian distribution. Nonetheless, there are fundamental limitations that must be recognized. The present focus on probabilistic analysis should be balanced by more research on statistical inference. It is acknowledged that statistical inference for correlated data is a challenging problem, but its practical significance is obvious.