Classical Statistics, Random Distributions, Normal And Lognormal Theory - 2.1 General

To determine the characteristics of a mineral deposit, the usual practice is to take samples, analyse the properties of those samples and infer the characteristics of the deposit from these properties. This analysis can be done using statistical methods. In the present work we are concerned with two types of statistical approaches, classical statistics and spatial statistics. If one uses classical statistics to represent the properties of the sample values, the assumption is made that the values are realizations of a random variable. The relative positions of the samples are ignored, and it is assumed that all sample values in the mineral deposit have an equal probability of being selected. The likely presence of trends, zones of enrichment, or pay shoots in the mineralization, is ignored. The fact that two samples taken close to each other are more likely to have similar values than if taken far apart is also not taken into consideration. In contrast, spatial statistics will be used if one chooses to consider that the sample values are realizations of random functions. On this hypothesis, the value of a sample is a function of its position in the mineralization of the deposit, and the relative position of the samples is taken into consideration. The similarity between sample values is quantified as a function of the distance between samples and this relationship represents the foundation of spatial statistics. There are few situations where classical statistics can be used. The assumption that all sample values in the mineral deposit have an equal likelihood of being represented will be satisfied only if the sample values are randomly distributed, or if the sample positions are random. Sample values are in fact never randomly distributed within a mineral deposit. Further- more, geologists usually avoid taking samples at random (random sampling), as it is correctly accepted that samples located on a regular grid, or approximately on a regular grid, give more information than randomly located samples. In practice, classical statistics should be used only in the early stages of exploration, when the number of samples available is relatively small and the distances between samples are large. In these circumstances, and whenever the information available is not sufficient to permit the use of spatial statistics, application of the methods described in this chapter is justified.