Comparing ordinary kriging interpolation variance and indicator kriging conditional variance for assessing uncertainties at unsampled locations

摘要

This paper presents an investigation into measures of the reliability associated with both ordinary kriging and indicator kriging. Ordinary kriging is a well known estimation method which is based on minimization of the error variance. This estimation method provides the traditional kriging variance and the interpolation variance as well. Indicator kriging is a method used to compute conditional probability at an unsampled location that the unknown value is no greater than a given cutoff value. Actually indicator variables are determined for each cutoff by means of a nonlinear transform. From conditional cumulative distribution built from assembling the conditional probabilities computed for all cutoff values, one can derive the conditional expectation (E-type estimate) and the conditional variance. Interpolation variance and conditional variance were computed from a sample data set drawn from an exhaustive data set. From the exhaustive data set true variances were calculated. Then, sample variances are compared with true variances. Both sample variances present good correlation with the true variance, but the conditional variance was slightly better than the interpolation variance.