Issue 11, p. 41 (2022)


Extensions to the Theory of Sampling 2. The Sampling Uncertainty (SU), and SU as alternative to variographic analysis

  • Bo Svensmark  
 Corresponding Author
Department of Plant and Environmental Sciences, University of Copenhagen, Faculty of Science, Thorvaldsensvej 40, DK-1871, Frederiksberg C, Denmark
[email protected]
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In the Theory of Sampling the Grouping and Segregation Error (GSE) is expressed relative to the Fun-damental Sampling Error (FSE) by GSE = Y·Z·FSE. Unfortunately, estimation of Z seems difficult or impossible. The problem seems to be the attempt to link GSE to FSE. However, the sampling uncertainty due to FSE + GSE can be estimated from the distributional heterogeneity, with a small modification, by a new function, the Sampling Uncertainty (SU) proposed here. SU is calculated from the spatial distribution of the analyte in a manner similar to cyclic convolution. The new method was validated by a riffle splitter mass reduction experiment and by variographic analysis of theoretical data. For 1-dimensional sampling SU is shown to be better than variogram integration in case of cyclic or non-stationary variations and by being independent of the nugget effect when the nugget effect is close to zero. Thus, the extensions allow accurate predictions of the correct sampling uncertainty for 1-dimensional sampling and are proposed as a supplement to variographic analysis. The rationale for using SU is to be able to set up plausible theoretical scenarios for a sampling problem, and to predict the effect of variations in sample size, increment number, increment orientation and sampling method (random systematic, stratified random, random or single increment sampling). SU can also give numeric results for 2-dimensional sampling. The use of SU will mainly be for teaching and for a quantitative understanding of Theory of Sampling and of the benefits of compositional sampling.




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