Generating inter-correlated observations under a specified spatial model

Abstract

The requirement to generate this random process needs only to define the variance-covariance matrix of the random process. Since the random process is defined in three dimensional space, then we can use a spatial model. One of the spatial model to define the random process is in the form of variogram, which is a function of distance between pairs of observations. The variance-covariance matrix may be determined in relation with two other properties, those are correlogram and covariogram. The simulation process was started by generating a random points within a particular shape of region. The locations are uniformly distributed within the region. Lets V is a variance-covariance matrix of the random process Y[L]. The random process Y[L] may be defined by the semivariogram model y(dij). The dij is a Cartesian distance between two different individual within domain D of boundary B. The distribution-based approaches can be applied to generate random observations using Choleski decomposition.