C14 | Improving inference based on sampling plan results using the Bayesian beta-binomial model: the case of the algal biotoxin monitoring plan for natural beds of Chamelea gallina clams

C. Ciccarelli¹, A. M. Semeraro¹, V. Di Trani¹, M. Leinoudi², G. D’aurizio³, F. Barchiesi⁴, S. Gentili⁵, E. Ciccarelli⁶. | ¹Azienda Sanitaria Territoriale Ascoli Piceno, ²Chimico libero professionista, ³Regione Marche – Agenzia Regionale Sanitaria, ⁴Istituto Zooprofilattico Sperimentale dell’Umbria e delle Marche, ⁵Veterinario libero professionista, ⁶Biologo libero professionista.

Purpose. This paper illustrates how the adoption of a Bayesian beta-binomial model can improve statistical inference techniques and, consequently, the reliability of decisions based on the outcomes of food safety sampling plans. This model provides, in an intuitive but rigorous way, a useful tool for updating probabilistic beliefs after observing data, while offering great flexibility in quantifying uncertainty using probability theory. As a case study, the framework was applied to monitoring data, collected from 2015 to 2024, on the level of algal biotoxins detected in Chamelea gallina clams harvested from classified production areas in the Marche Region. Methods. Starting from several initial hypotheses, which reflected the known low tendency, albeit with limited information in the scientific literature, of C. gallina to accumulate algal biotoxins (confirmed by the absence of RASFF alerts), the Bayesian beta-binomial model was used to assess the impact of the above-mentioned ten-year monitoring results in modifying or not modifying these initial hypotheses. The model was calibrated using Bayes' theorem, which employs the laws of probability to update the prior distribution, simplifying the execution of the necessary calculations. Results. The application of the Bayesian beta-binomial model made it possible to estimate the probability that Chamelea gallina clams from classified harvesting areas in the Marche Region could accumulate algal biotoxins in quantities exceeding the quantification limit of the analytical method used for detection, balancing the uncertainty and variability of the data obtained from the monitoring covered by the case study. The results showed that this model allows for accurate and reliable estimates of the probability of finding significant levels of contamination and improves the ability to correctly identify high-risk clam beds. The framework also demonstrated flexibility in its application: new data can be easily incorporated, making monitoring dynamic and adaptive. Conclusions. The use of the Bayesian beta-binomial model offers a significant advantage over traditional methods of analysing data obtained from sampling plans, thanks to better quantification of uncertainty and continuous updating of estimates, contributing to more informed and timely decisions in risk management. In the case study analysed, even starting from conservative initial assumptions and with a limited amount of data, it emerged that the probability of exceeding the quantification limit for algal biotoxins in clams from the Marche region is extremely low.