Knowledge base development from data for modern geostatistics

One main objective of environmental modeling is to produce useful maps of constituents over some spatiotemporal domain of interest. Modern geostatistical methods can be applied to produce such maps by (1) considering general knowledge such as governing relationships or statistical moments to rather (2) eliminating from consideration those otherwise plausible events that are deemed inconsistent with the available data, and then (3) reassigning probabilities to the remaining events to yield posterior probabilities that are consistent with the available data. Maps of expected values and associated confidence sets can then be prepared from computed posterior distributions. In support of such mapping efforts, knowledge base development on the basis of available data is important and is facilitated by original contributions regarding (1) the development of available uncertain (soft) information into suitable probabilistic form that can be assimilated as specific knowledge through Bayesian conditionalization, and (2) the inference of statistical moments to be accounted for as general knowledge based on available specific knowledge. Development of soft data in probabilistic form is demonstrated through regression methods applied to conventional environmental data and through generalized defuzzification of simulated fuzzy data. Straightforward inference of correlation structure based on soft data expressed in probabilistic form is shown to rely on an assumption that available soft data were independently obtained, in which case it is possible to infer correlation structure based on the respective means as hard data equivalents. The common estimator of the semivariogram is shown to depend on an assumption of a regular point pattern of sample locations that is violated by most environmental data sets. To address this problem a modified estimator of the semivariogram that incorporates declustering weights is presented and demonstrated. Thus this work extends the methods of modern geostatistics to be more widely applicable to environmental data sets.