Note on the correction of negative measured values if the measurand is nonnegative

• Published in: Accreditation and quality assurance 2014-04, Vol.19 (2), p.81-85
• Main Author: Wilrich, Peter-Th
• Format: Article
• Language: English
• Subjects: Analytical Chemistry; Bayesian analysis; Bias; Biochemistry; Chemistry; Chemistry and Materials Science; Commercial Law; Ecotoxicology; Food Science; General Paper; Marketing; Mean; Normal distribution; Radioisotopes; Random variables; Standard deviation
• ISSN: 0949-1775; 1432-0517
• DOI: 10.1007/s00769-013-1028-1

Often, the concentration of a substance or the activity of radionuclides in a sample is measured indirectly as the difference between signal and noise, i.e. the difference between the measured value obtained at the sample and that obtained at a sample not containing the substance or the radionuclides (blank sample). The difference can be negative, especially if the concentration or the activity is low. Since a negative measurement result for a nonnegative measurand does not make sense, measured values must be corrected to nonnegative measurement results. Weise et al. and Korun/Maver Modec use a Bayesian approach in order to obtain a nonnegative estimate of the nonnegative measurand. Their estimate is the mean of the posterior distribution. Korun and Zorko modify this estimate slightly and obtain a less biased estimate. In this paper, it is proposed to use the mode of the posterior distribution instead of the mean. The resulting estimate is equal to the measured value if it is nonnegative and 0 if it is negative. This estimate has three advantages: it is extremely easy to calculate, it is less biased than the posterior mean proposed in the other papers, and it does not use the known standard deviation, i.e. it can also be used if the standard deviation is unknown.