Geostatistical modelling of spatial potentials

Discrete systems often manifest themselves as spatially continuous phenomena over a region of space. A system is studied by measuring the corresponding spatial phenomenon at some locations over space and by drawing conclusion from the estimated spatial surface. In many cases, the discrete nature of the system has to be taken into account as well as the interaction between the system and the measuring instruments used to collect the data. As a consequence, neither the classic geostatistical models nor the classic methods provided by the point process statistics are suitable for estimating the phenomenon spatial surface. In this paper, the general problem is studied by introducing a novel paradigm which justifi es the de finition of a new class of geostatistical models able to address both the discreteness of the system and its interaction with the measuring instruments. The proposed class of models find application in many scienti c fi elds including both the natural and the social sciences. The model estimation problem is solved in detail and a case study related to a geomarketing application is addressed.