Bi-Gaussianized calibration of likelihood ratios

Abstract

For a perfectly calibrated forensic evaluation system, the likelihood ratio of the likelihood ratio is the likelihood ratio. Conversion of uncalibrated log-likelihood ratios (scores) to calibrated log-likelihood ratios is often performed using logistic regression. The results, however, may be far from perfectly calibrated. We propose and demonstrate a new calibration method, “bi-Gaussianized calibration,” that warps scores toward perfectly calibrated log-likelihood-ratio distributions. Using both synthetic and real data, we demonstrate that bi-Gaussianized calibration leads to better calibration than does logistic regression, that it is robust to score distributions that violate the assumption of two Gaussians with the same variance, and that it is competitive with logistic-regression calibration in terms of performance measured using log-likelihood-ratio cost (Cllr). We also demonstrate advantages of bi-Gaussianized calibration over calibration using pool-adjacent violators (PAV). Based on bi-Gaussianized calibration, we also propose a graphical representation that may help explain the meaning of likelihood ratios to triers of fact.