The SIMNORMAL Procedure

Introduction

There are a number of approaches to simulating a set of dependent random variables. In the context of spatial random fields, these include sequential indicator methods, turning bands, and the Karhunen-Loeve expansion. See Christakos (1992, Chapter 8) and Deutsch and Journel (1992, Chapter 5) for details.

In addition, there is the LU decomposition method, a particularly simple and computationally efficient for normal or Gaussian variates. For a given covariance matrix, the $\bL \bU =\bL \bL ’$ decomposition is computed once, and the simulation proceeds by repeatedly generating a vector of independent $N(0,1)$ random variables and multiplying by the $\bL $ matrix.

One problem with this technique is that memory is required to hold the covariance matrix of all the analysis and conditioning variables in core.