## 2 Archaeological Questions/Archaeometric Answers
### Provenance: Importation Versus Local Production  
As previously said, the aim of this paper is to integrate the data on the Apulian red figure pottery obtained on finds from specific sites into a more cohesive picture. The chemical data obtained for each archaeological site have been then assembled into a single matrix and analyzed using traditionally (DA) and innovative (NLPCA) multivariate statistical analysis techniques. Preliminary investigations were conducted on the original matrix of 30 chemical elements (Fe, Al, Mg, K, Ti, Na, Ca, Mn, Co, Cu, Pb, Ni, Sr, Cr, Ba, Sn, Zn, Li, V, Zr, Cs, La, Ce, Sn, Tb, Yb, Lu, Eu, Nd, Dy). Statistical technique, based on comparing the means and the variances of the different variables, was applied as a criterion to reject those chemical elements that introduce noise and make more difficult the exploratory analysis and the subsequent classification. Therefore, statistical treatment was performed on a concentration matrix of 11 chemical parameters (Fe, Al, Mg, K, Ti, Na, Ca, Mn, Ni, Sr, Cr). To clarify if Apulian items were locally produced or imported, a bibliographic research on compositional data of Attic red figure finds has been carried. The statistical treatment comparison to detect similarities and/or differences has been performed regards Attic samples coming from different Greek sites -Atene, Perati, Rafti, Thorikos, Aigina, Megara- [51], whose chemical bulk data have been obtained by applying Atomic Spectroscopy techniques and are thus immediately comparable to our Apulian ones. Common parameters are Fe, Al, Mg, Ti, Na, Ca, Ni, Cr, which unfortunately implies that useful information obtainable by other minor and trace elements contents are missing. Results (Figure 6a) highlight a strong compositional diversity of ceramic bodies of finds from Apulian sites and Greek ones, so making it possible to discriminate between Apulian and Attic production, allowing to identify imported and locally produced objects. For example, it was possible to confirm the importation of a sample (code T38, inventory number 227208), excavated in Taranto which, based on archaeological investigations, was believed to be made in Greece. Its score position, in fact, inside the Attic cluster and far from the Apulian one, shows a greater compositional similarity to the Attic samples than to the Apulian ones. The same conclusion can be deduced using a QDA model computed by considering the Attic and Apulian classes a priori. In the table (Figure 6b), the parameters evaluating the quality of the model are summarized. The NER shows that the 99.62% of the total samples are correctly classified. Output analysis highlights that only the sample T38 is classified in another class. The mineral-petrographic investigations [29], highlighting for T38 a mineralogical composition dissimilar to Apulian samples, strengths the hypothesis of a sample importation. Excluding samples of suspected imports, all the analyzed Apulian samples have been treated by NLPCA. The results highlight three different clusters that follow the ancient division of Apulia (Peucetia, Messapia and Daunia) (Figure 7a), proving the existence of a polycentric production [99]. The fitting values in the terms of \(R^{2}\) and Lof, 0.96 and 0.19, respectively, indicate that the better model fitting is achieved when at least the first  
Figure 6: **(a)** Scores plot of the NLPCA model related to finds from Apulia (red) and Greece (blue), (\(R^{2}\) 0.89 and Lof 0.34). Sample T38 is marked with a star. (b) Confusion matrix and NER value obtained with the application of QDA on data. 3 principal components are considered. Compositional data matrix included data relating to finds which historical sources indicate to come from Ruvo di Puglia: the samples of the [PERSON] collection, kept at Gallerie d'Italia Leoni Montanari [28] in Vicenza (Italy) and the two vases kept at MANN [27]. LDA application shows that the 98.62% of the samples are correctly classified. All 52 Daunian and 38 Messapian samples are recognized to be belonged to the a priori classes.