Comparison of Cokriging with an LMC versus the Intrinsic Model

The major obstacle to extensive use of cokriging for integration of multiple data types in estimation is the requirement of modeling a positive definite covariance matrix of size K by K including up toK different terms if K coregionalized variables are considered. In practice, this matrix is modeled using a linear model of coregionalization (LMC); each covariance is modeled by a different linear combination of the same basic covariance functions. Oftentimes, sampling of the secondary variable is much more extensive than that of the primary variable, often, the secondary variable is exhaustively sampled (sampled at each node where the primary variable is to be estimated). In such cases, only the secondary data at the estimation location (‘colocated’ value) could be retained in estimation. The underlying Markov-type hypothesis is that the collocated primary data screens out all further away primary information. Under Markov hypothesis, all that is needed to perform estimation is the primary covariance function and the correlation coefficient between primary and secondary data. An intrinsic correlation model (ICM) was proposed for modeling the covariance matrix. The intrinsic correlation model is obtained when the direct and cross covariance functions are all proportional to the same underlying spatial correlation function. Although ICM appears similar to a Markov models, it makes greater use of the secondary data and does not result in variance inflation. This paper is aimed at comparing and analyzing different correlation models, that is, linear model of coregionalization, intrinsic correlation model and Markov model based on a small comparative example.