A comparison of parametric and non-parametric methods for modelling a coregionalization

Abstract

Two methods for modelling a coregionalization were compared, the traditional parametric linear model of coregionalization (LMCR) and a non-parametric method based on a Fourier transform of the empirical (cross-) correlogram maps. The methods were compared in terms of how well they fit the experimental correlograms, and the prediction quality of their co-kriged estimates. Three datasets were compared, each representing different situations where we might use co-kriging. We found that both methods were somewhat restricted in how well they could represent the experimental correlograms because of the constraint that any coregionalization model must be positive-definite. There was little to distinguish between both methods in terms of how well the models fitted the raw correlogram data. The cokriged estimates from both methods were very similar in terms of their accuracy however the kriging variances from the LMCR were a better reflection of the prediction error. The non-parametric modelling is substantially faster than modelling the LMCR so if the only interest is in obtaining cokriged estimates then it should seriously be considered. In cases where the kriging variances are of interest then the LMCR should be used.