Iii. the Basic Equations of the Bme Mapping Method

The methods of classical geostatistics were primarily developed under a set of constraining assumptions (linear estimator, measurements are exacts, etc.) and they lack the theoretical underpinnings and practical flexibility to incorporate the many sources of information available in modern days sciences (such as physical laws, empirical models, higher statistical moments, uncertain information). The physical knowledge base available in modern geostatistics was defined in the previous chapter as the union of general knowledge describing the Space/Time Random Field (S/TRF) X( p), and specificatory knowledge which include exact observed values (hard data) and uncertain measurements (soft data). In this chapter I present the epistemological tools of the Bayesian Maximum Entropy (BME; Christakos, 1990, 1992) method of modern geostatistics which are used to process the total knowledge base available. The epistemological approach of BME may be represented by the use of two operators; the first for processing general knowledge, and the second to process specificatory knowledge. The result of the knowledge processing operators is a BME posterior pdf, which describes completely the S/TRF at the estimation point. The BME posterior pdf provides a complete picture of the mapping situation, and it provides as well different estimators of the S/TRF and their associated estimation uncertainty, which are useful for mapping purposes.