Measurement of small quantities: further observations on Bayesian methodology

This article discusses the measurement of the sum of small positive quantities each estimated in separate analyses. It extends criticism recently given of 'objective Bayesian' methodology (Accred Qual Assur 15:181-188, 2010) and identifies two troublesome effects: the inherent bias in an analysis for a single quantity is compounded when the measurand is the sum of such quantities, and the precaution of overestimating measurement variability can actually make the resulting interval of measurement uncertainty less reliable! Unacceptable results are obtained. A cause of this behavior is identified, and a distinction between 'objective' and 'subjective' Bayesian statistics is discussed.