Uncertainty in repeated measurement of a small non-negative quantity: explanation and discussion of Bayesian methodology

This article considers the problem of uncertainty evaluation when there are repeated measurements of a small quantity known to be non-negative. A solution to this problem has recently been put forward by the Analytical Methods Committee of the Royal Society of Chemistry (Accred Qual Assur 13:29–32). The Bayesian statistical basis of this solution is explained and discussed. It is shown that the performance of this procedure can be poor in an important subset of measurement situations.