## 4 Discussion  
The characterization of protected designation of origin is a critical factor for the viability of local products where the increased production cost is counterbalanced by a higher price. At the same time, PDO products become the target of fraudsters who want to benefit from the higher value, and fake products of different origins. Fraudsters hide behind the \"declarative\" nature of the designation characterization. With the proposed model and methodology, we quantified the clear difference of the bottarga from Messolongi in general, while at the same time we turned it to decision mechanism for the certification of individual samples. Stable isotope ratios of \(\delta^{34}\)S\({}_{\text{V-CDT}}\) (%) are very distinct for the case of the Bottarga originated from the area of Messolongi. Carbon and nitrogen stable isotopes depend on nutrient uptake, digestion, and metabolism of the organisms [42; 43; 44]. Hence, the diet of each organism can explain the differences in these results. On the other hand, the \(\delta^{34}\)S\({}_{\text{V-CDT}}\) ranged from 4.53% to 16.03% which are typical values for marine fish. Similar results for \(\delta^{34}\)S\({}_{\text{V-CDT}}\) (4.6-20.1%) have been reported from [PERSON] et al. (2013) [45]. However, the lowest value has been reported for Messolongi samples. Messolongi lagoon is a shallow area connected with two narrow openings in the north side with Etoliko lagoon and in the south with Gulf of Patras allowing seawater influx in the lagoons. In addition, two major rivers of the area (Acheloos and Evinos), have also participated in the formation of the lagoons through the deposition of sediment. Towns and highly cultivated agricultural areas in the vicinity of the lagoons produce an influx of sewage and irrigation run-off rich in nutrients. The influx of nutrients causes a high oxygen demand during decomposition of the organic matter. Moreover, large gypsum (CaSO\({}_{4}\) 2H\({}_{2}\)O) deposits to the north-west  
Figure 8: Decision confidence level of probabilistic model that incorporates measurement error of a sample has been collected from Messolongi (blue line). of the Etoliko lagoon generate hydrogen sulfide in the hypolimnion (gypsum dissolves in water to produce sulphate ions (SO\({}_{4}\))\({}^{2-}\) which under anaerobic conditions are reduced to elemental sulfur and hydrogen sulfide). The organic and inorganic material rich in sulfur compounds is broken down by bacteria present on the lagoon bottom producing sulfides. The bacteria under anaerobic conditions produce S\({}^{-2}\), HS\({}^{-}\), and H\({}_{2}\)S with the reduction of sulfur. Hydrogen sulfide can either be oxidized to elemental sulfur by sulfur-bacteria or be released into the surrounding water [46; 47]. This special condition affects the ratio of sulfur isotopes. According to [PERSON] et. Al., irradiated plants with roots immersed in (HSO\({}_{3}\))\({}^{-}\) and (SO\({}_{4}\))\({}^{2-}\) solutions at concentrations found in nature emit H\({}_{2}\)S from their leaves, and that H\({}_{2}\)S emitted contained more \({}^{32}\)S and less \({}^{34}\)S, namely, lower \({}^{34}\)S\({}_{\text{V-CDT}}\) values, in comparison to irradiation solutions [48]. Therefore, the high H\({}_{2}\)S concentration present in the Etoliko and Messolongi lagoon's bottom layer has, as a result, low \({}^{34}\)S\({}_{\text{V-CDT}}\) (%) values. The forementioned reason explains the great difference of Messolongi \({}^{34}\)S\({}_{\text{V-CDT}}\) values from the corresponding values of the other areas helping to the authentication of bottarga products originated from Messolongi by using a probabilistic machine learning approach to cope with small number of samples. Conceptualization, G.T., A.P. and A.L. ; methodology, E.P., E.C.M., K.K. and A.-A.T.; software, G.T., A.-A.T. and A.Z. ; validation, E.P., E.C.M. and K.K. formal analysis, G.T. and A.K. ; investigation, E.P., E.C.M. and K.K. ; resources, A.P. and A.L. ; data curation, E.C.M., A.Z., E.P. and G.T. ; writing--original draft preparation, G.T., A.-A.T. and A.K.