Abstract

Abstract Often, there are two streams in statistical research -one developed by practitioners and other by main stream statisticians. Development of geostatistics is a very good example where pioneering work under realistic assumptions came from mining engineers whereas it is only now that statistical framework is getting more transparent. The subject with statistical emphasis has been evolving, as seen by various excellent books from statistical sides (Banerjee, S., Introduction It is well known that the maximum likelihood (ML) method is a powerful statistical tool in estimation for parametric models. The method of maximum likelihood was introduced by R.A. Fisher as early as 1931 but its application in geostatistics for inference of variogram parameters has been slow and it was first introduced by Mardia (1980) -incidently, this paper was presented to the Geological Congress in Paris in There is no doubt that the availability of cheap and powerful computers has increased the interest in ML applications. With spatially correlated data, the maximization of the likelihood requires considerable computer power mainly for two numerical operations: matrix inversion and maximization in multidimensional parameter spaces. The method of ML in geoestatistics can be used complementary with the well established method among practitioners of graphical variogram modelling. The variogram plots should be used as a tool for getting hints on selecting a model and the actual unknown parameters of the model could be estimated by ML. Furthermore, ML provides an uncertainty of the estimated parameters what may be used to decide if point estimates are sufficiently accurate or if interval estimation (giving a region of suitable parameters) is more adequate. We discuss various practical and theoretical problems with MLE (The talk will have several illustrated examples). The conclusion is that the ML method is feasible for geostatistics; it can be implemented efficiently and provides a powerful tool for geostatistical inference. It provides a complete approach to variogram inference offering methodology for model selection, statistical inference and providing measures of uncertainty of the estimated parameters. Historically, the following observation of Watson (1986) is a key in understanding the development of statistical geostatistics: "In the mid 1970s the work of Georges Matheron and Jean Serra of the Center for Mathematical Morphology at the Paris School of Mines, attracted my attention. They seemed to be breathing new life into the application of statistics to geology and mining. As a result, I spent a lot of time persuading Englishspeaking geologists and statisticians that this was so, while trying to persuade the Fontainebleau School to integrate their writings with that of the anglophones! Our geologists receive very little mathematical