White marbles in Roman architecture: Electron paramagnetic resonance identification and bootstrap assessment of the results

On the basis of a previously reported spectroscopic and petrographic database, a general procedure for determining the provenance of white marbles is presented and used to establish a classification rule for the marbles most used in Roman architecture. The rule, based on a data set including seven groups (Carrara, Naxos, Paros, Pentelicon, Proconnesus and Thasos, calcitic and dolomitic marbles) and 712 samples, uses quadratic discriminant analysis and a set of four spectroscopic and two petrographic variables, after logarithmic transformation. The performance of the rule, obtained by resubstitution, is 93.3%. Validation of this result, carried out using the bootstrap technique, after briefly introducing the method, indicates that the resubstitution bias is 1.4%, with a final unbiased performance of about 92%. The bootstrap result agrees satisfactorily with alternative bias estimates (jackknife, cross-validation). Problems connected with the assignment of sets of unknown samples and the methods used for distinguishing reliable from doubtful assignments are discussed.