Numerical likelihood ratios outputted by LR systems are often based on extrapolation: When to stop extrapolating?

A recent trend in forensic science is the development of objective, automated systems for the comparison of trace and reference material that give as output numerical likelihood ratios (LRs). For well discriminating LR systems, often the probability of the evidence given one or the other hypothesis depends on the density from the tail of a probability distribution. The models for probability distributions are trained by data. Since there is no proof of the applicability of the models beyond the data range, LR systems are sensitive to extrapolation errors. Given the unknown behavior in the tail region one may define the problem as when to stop extrapolating. When applied to LR systems, this leads to limit values of the likelihood ratio (e.g. a minimum and a maximum value of the LR outputted by the LR system), depending on the sizes of the validation datasets used. The solution proposed in this paper to determine these limits is based on the normalized Bayes error-rate [1] in combination with the introduction of misleading LRs with increasing strength.