Bounding as a remedy for reference-label error in Cllr validation of forensic likelihood-ratio systems

The log-likelihood-ratio cost ( C llr ) is the standard metric for validating automated likelihood-ratio (LR) systems in forensic science, justified by its being a strictly proper scoring rule. Several studies have developed calibration diagnostics, protocols and surveys of reported values; however, each presumes the reference set carries correct labels, whereas forensic reference sets rest on ground truth by proxy or examiner adjudication. Based on the literature, the sensitivity of C llr to such error is unquantified, because measuring it requires the true LR, unobtainable in real forensic domains. The aim of this study is to quantify that sensitivity against known true likelihood ratios, to locate where it is severe, to derive the optimal bound, and to provide a contamination diagnostic needing no clean-label baseline. The optimal system, computed in closed form from a specified generator, was scored against labels carrying error rates to 10 per cent and compared against two reconstructions of the Empirical Lower and Upper Bound (ELUB) procedure and four alternatives. The results show that at a mean absolute log 10 L R of 17.2 a 3.5 per cent error rate inflates the cost thirtyfold and scores it as worse than uninformative, whereas below about six inflation stays at or below 1.4-fold. Mislabelled items carry 62.8 to 99.6 per cent of the cost, and parameterising the bound by each arm's contamination predicts the empirical optimum almost eightfold more accurately than the nominal error rate does. Bounding is therefore necessary for valid C llr reporting on unverified reference sets.