Assay of Material

The first field which was studied was the assay of material whose spatial distribution is unknown. Consider, for instance, a small quantity of a toxic or radioactive element dispersed within a matrix of other material. The aim is to determine the total quantity of the toxic material – the analyte – regardless of its spatial distribution, which is unknown. The presence of the analyte can be detected by radiation which it emits either passively or in response to activation. However, this radiation is absorbed as it traverses the matrix. A detector senses the radiation, and the greater the quantity of analyte, the larger the signal in the detector. However, the magnitude of the signal depends strongly on the spatial distribution of the analyte because of absorption in the matrix. This spatial distribution may be quite complicated, and is unknown. A probability distribution could describe the uncertainty in the spatial distribution. However, choosing which probability distribution to use requires either strong assumptions about the manner in which the analyte was dispersed, or extensive data. The research challenge was to address the assay problem without requiring extensive probabilistic information. The central questions are: Where to place the detectors? How many detectors to use? What is the value of the marginal detector? How to deduce the quantity of analyte from the resulting measurements? The study of these questions led to the early version of an info-gap model of uncertainty, though it was not called that at the time. (Ben-Haim, 1985).
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