Contents lists available at ScienceDirect Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem Bayesian treatment of results from radioanalytical measurements. Effect of prior information modification in the final value of the activity M. Barrera a , I. Lira b , M. Sánchez-Sánchez c , A. Suárez-Llorens c, ⁎ a Escuela Superior de Ingeniería, Universidad de Cádiz., Avda. Universidad de Cádiz 10, 11519 Puerto Real, Cádiz, Spain b Pontificia Universidad Católica de Chile, Dept. of Mechanical and Metallurgical Engineering, Vicuña Mackenna, 4860 Santiago, Chile c Facultad de Ciencias, Universidad de Cádiz., Avda. Rep. Saharaui s/n, 11510 Puerto Real, Cádiz, Spain ARTICLEINFO Keywords: Robust Bayesian analysis Radiation measurement Class of priors Radionuclide analysis Proficiency tests Uncertainty of measurement ABSTRACT We address the problem of evaluating measurements of radionuclide activity concentration from a robust Bayesian perspective. As shown in previous studies, Bayesian incorporation of available prior information on the activity levels, together with the measured values, leads in general to an improvement in the quality of radio- analytical results. Since the specific form of the employed prior is a critical aspect of the Bayesian framework, in the present paper we distort the prior distribution in order to evaluate how it influences the final activity estimate. We applied this procedure to inter-laboratory proficiency test data obtained by the laboratories that perform radiochemical analysis for the Spanish radioactive monitoring network. We found that in the present application the Bayesian methodology is indeed robust, as modifying the specific form of the prior has little effect on the activity estimate. Similar sensitivity analysis could be applied to the Bayesian evaluation of measurements of other quantities for which prior knowledge is available. 1. Introduction Bayesian statistics constitutes a powerful methodology to evaluate measurement data. One of its advantages is that it allows incorporating prior knowledge (prior information) about the specific quantity under study (in our context, the mensurand). The use of this prior informa- tion, together with the experimental value of the measurement per- formed, can be used to obtain in general a better estimation of the physical quantity under study, see for example (Mazrou and Bezoubiri, 2018). In the scope of radionuclide activity measurements of environ- mental samples, previous studies (Barrera et al., 2007) have shown the effectiveness of the Bayesian methodology; see also ISO (2005); Grientsching and Lira (2012); Korun et al. (2014); Mathews and Gerts (2008); Rivals et al. (2012); Sterlinski (2008); Weise et al. (2006) and Weise et al. (2009) for related analyses oriented to the calculation characteristic limits such as decision thresholds, detection limits and confidence limits. A thorough review of the Bayesian approach can be found in Bernardo (2003, 2005); Gelman et al. (2004); Lira and Grientsching (2010); Lira and Wöger (2006) and Silva and Skilling (2006); also ISO (2008) and Romero (2004) provide some guidance on the uncertainty components of the measurement processes. However, paradoxically, the advantage brought about by the introduction of prior information is also to some extent a disadvantage of the Bayesian fra- mework: if using other priors is acceptable, the one selected may appear to be somewhat arbitrary. This is precisely the problem addressed by Robust Bayesian Analysis (Ríos Insua and Ruggeri, 2000), also called Bayesian Sensitivity Analysis, which quantifies and interprets the un- certainty induced by incomplete knowledge about the precise details of the analysis. Thus, the present work is intended to clarify and to support the Bayesian treatment of prior information from a robust viewpoint in the context of radioanalytical measurements. As in Barrera et al. (2007), the case studied below is the Inter-la- boratory Proficiency Test periodically organized among the Spanish environmental radioactivity laboratories that perform radiochemical analysis for the Spanish radioactive monitoring network, see (Romero and Ramos, 2000). The scheme of these exercises consists in the de- termination of different radionuclide activities in a test sample dis- tributed to the laboratories of the network. If is the parameter that represents the actual unknown activity of a certain radionuclide, its state of knowledge before any measurements are taken is encoded by a probability density function (PDF), denoted by (), which is termed the prior. Which is the prior in our case? At the beginning of the exercise, when each laboratory receives the sample, the coordinator that assesses https://doi.org/10.1016/j.radphyschem.2018.11.023 Received 19 July 2018; Accepted 23 November 2018 ⁎ Corresponding author. E-mail addresses: manuel.barrera@uca.es (M. Barrera), ilira@ing.puc.cl (I. Lira), marta.sanchez@uca.es (M. Sánchez-Sánchez), alfonso.suarez@uca.es (A. Suárez-Llorens). Radiation Physics and Chemistry 156 (2019) 266–271 Available online 28 November 2018 0969-806X/ © 2018 Elsevier Ltd. All rights reserved. T