Estimation of Conditional Non-Gaussian Translation Stochastic Fields

Abstract

A theoretical formulation is presented to estimate conditional non-Gaussian translation stochastic fields when observation is made at some discrete points. The formulation is based on the conditional probability density function incorporated with the transformation of non-Gaussian random variables into Gaussian variables. A class of translation stochastic fields is considered to satisfy the requirement of nonnegative definite for the correlation matrix. A method of conditional simulation of a sample field at an unobservation point is also proposed. Numerical examples were carried out to illustrate the accuracy and efficiency of the proposed method. It was found that: 1) the optimum estimator at an unobserved point based on the least-mean-square estimation is equal to the conditional mean; 2) the estimated error variance is dependent on the locations of sample observation, but independent of the values of observed data; and 3) the conditional variance does not coincide with the estimated error variance. These findings, which have already been confirmed for a lognormal stochastic field by the Kriging technique are clearly different from the results of conditional Gaussian stochastic fields.