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The quantitative assay of material arises in numerous branches of science and industry. In many applications, the assayed sample is heterogeneous, showing variation throughout the sample of density or composition. Such structuring of the sample complicates the calibration of the measurement. It may be feasible to calibrate directly by altering the sample itself, for example by spiking the sample with a known quantity of the analyte. However, for solid samples this may be impossible, or for remote samples such as in situ bore-hole geological assays this may be impractical, or for medical assays on living human subjects this may be undesirable for health reasons. On the other hand, preparation of standardized samples which simulate the spatial structure of the assayed sample may be technically quite difficult. A more serious problem arises when the spatial structure of the sample is unknown, such as for a subterranean mineral deposit. Determination of the spatial structure of the sample may be much more challenging than the assay itself. Finally, the spatial structure may vary randomly throughout an ensemble of samples. Random variation of the spatial structure is observed in the assay of fissile materials produced in various stages of the nuclear fuel cycle, in parameter-estimation of flowing fluids, in medical assays and in geological and meteorological studies.
KeywordsMedical Assay Annular Flow Nuclear Fuel Cycle Spatial Uncertainty Spatial Randomness
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