Bayesian approach to uncertainty evaluation: is it always working?

¹ Politecnico di Milano, DEIB -Dipartimento di Elettronica, Informazione e Bioingegneria, P.za Leonardo da Vinci 32, 20133 Milano, Italy;
² Politecnico di Milano, DENG -Dipartimento di Energia, Via Lambruschini 4, 20156 Milano, Italy

^* Corresponding author: simona.salicone@polimi.it

Abstract

Since the GUM has been published, measurement uncertainty has been defined in terms of the standard deviation of the probability distribution of the values that can be reasonably attributed to the measurand, and it has been evaluated using statistical or probabilistic methods. A debate has always been alive, among the metrologists, on whether a frequentist approach or a Bayesian approach should be followed to evaluate uncertainty. The Bayesian approach, based on some available a-priori knowledge about the measurand seems to prevail, nowadays. This paper starts from the consideration that the Bayesian approach is based on the well-known Bayes theorem that, as all mathematical theorems, is valid only to the extent the assumptions made to prove it are valid. The main question, when following the Bayesian approach, is hence whether these assumptions are satisfied in the practical cases, especially when the a-priori information is combined with the information coming from the measurement data to refine uncertainty evaluation. This paper will take into account some case studies to analyze when the Bayesian approach can be usefully and reliably employed by discussing the amount and pertinence of the available a-priori knowledge.