On the precision of systematic sampling: a review of Matheron's transitive methods

G. Matheron's theory ofregionalized variablesprovides a suitable basis for obtaining variance approximations for estimators of integrals from systematically sampled observations, with applications in geostatistics, image analysis, stereology and numerical quadrature techniques in general. The approximations are often fairly accurate for practical purposes. The methods are, however, not sufficiently widespread outside the field of geostatistics. The purpose of this paper is to present in an informal way thetransitivepart of the methods (relevant to the design‐based approach) and a number of stereological applications.