Bayesian uncertainty analysis under prior ignorance of the measurand vs. analysis using the Supplement to the Guide: A comparison
Blaza Toman, Clemens Elster
A recent supplement to the GUM (GUM S1) is compared with a Bayesian analysis in terms of a particular task of data analysis, one where no prior knowledge of the measurand is presumed. For the Bayesian analysis, an improper prior density on the measurand is employed. It is shown that both approaches yield the same results when the measurand depends linearly on the input quantities, but generally different results otherwise. This difference is shown to be not a conceptual one, but due to the fact that the two methods correspond to Bayesian analysis under different parametrizations, with ignorance of the measurand expressed by a non-informative prior on a different parameter. The use of the improper prior for the measurand itself may result in an improper posterior probability density function (PDF) when the measurand depends nonlinearly on the input quantities. On the other hand, the PDF of the measurand derived by the GUM supplement method is always proper but may sometimes have undesirable properties such as non-existence of moments.
and Elster, C.
Bayesian uncertainty analysis under prior ignorance of the measurand vs. analysis using the Supplement to the Guide: A comparison, Metrologia, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=900233
(Accessed November 30, 2023)