Disjunctive Kriging: 1. Overview of Estimation and Conditional Probability

The disjunctive kriging method described in this paper produces a nonlinear unbiased estimator with the characteristic minimum variance of errors. Disjunctive kriging is as good, or otherwise better than linear estimators in the sense of reduced kriging variance and exactness of estimation. It does not suffer from the difficulties associated with computing the conditional expectation and can be thought of as its estimator. Disjunctive kriging also provides an estimate of the conditional probability that a random variable located at a point or averaged over a block in two-dimensional space is above some specified cutoff or tolerance level and this can be written in terms of the probability distribution or the density function. The method has important implications in aiding management decisions by providing a quantitative input (which is not readily obtained from the linear kriging estimators), based on the available data, which is the best nonlinear unbiased estimator short of the conditional expectation. A major disadvantage in using disjunctive kriging is the increased computational time. This, however, is mitigated by increased information about the estimate.