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

Avoiding overstating the strength of forensic evidence: Shrunk likelihood ratios/Bayes factors

“…The procedure and its rationale are described in [13]. To implement the procedure, we need training data consisting of a set of likelihood ratio values known to be from same-origin comparisons and a set of likelihood ratio values known to be from different-origin comparisons (note that these are likelihood ratio values, not score values).…”

“…The tails of distributions are intrinsically sparsely sampled, hence probability density estimates in tail areas are susceptible to large fluctuations resulting from even small changes due to sampling variability. [13] proposes the imposition of upper and lower bounds on the value of the likelihood ratio. Values beyond the bounds are replaced by the values at the bounds.…”

Elemental Characterization of Printing Inks and Strengthening the Evaluation of Forensic Glass Evidence

“…Vergeer, et al and van Es, et al reported one method for calibration that involves the use of density models followed by the empirical lower and upper bound (ELUB) method to limit the LR output. [44][45] The distribution of the same-source LR scores (using the MVK model) was modeled using a double exponential decay and the distribution of the different-source LR scores was modeled using a KDE. 44 To compute the calibrated LR for a pairwise comparison, first the LR score is calculated using the MVK model.…”

“…The upper and lower limit for the calibrated LR is computed using a normalized Bayes error-rate (NBE) plot, which plots the log 10 EU ratio against the log 10 LR th . 45 The expected utility (EU) ratio is the ratio of the EU for the neutral case (in which the LR is always equal to 1) and the EU for the LR system: algorithm, which uses strictly proper scoring rules (SPSRs). 42,[139][140][141] The ELUB method described above includes one step for calibration and a subsequent step to limit the LR.…”

“…Vergeer, et al and van Es, et al reported one method of calibration that involves the use of density models followed by the empirical lower and upper bound (ELUB) method to limit the LR output. [44][45] This approach to calibration will subsequently be referred to as the "ELUB" method. The authors successfully applied the ELUB method to LRs calculated using the MVK model (also referred to as the two-level model).…”